Tjyylli

I suggest something line the following, so the wide terms are reduced.

documentclass{article}

%usepackage{amsmath}% Loaded by mathtools

usepackage{mathtools}



begin{document}



begin{gather*}

begin{align*}

g(eta,z)&=

parbox[t]{0.85displaywidth}{raggedright

$-306772802511648469920eta^4z^4+

762453974480763801600eta^5z^4-

1678626210368271790080eta^5z^3-

28510918043555533736160eta^4z^3+

11443138641451067779872eta^3z^3-

52164076923190540413504eta^2z^2-

78145258181161076156160eta^5z^2-

211306163712129371808450eta^4z^2+

228927087397104405937944eta^3z^2+

999881065017543109136462eta^3z-

317254092617698017425280eta^5z-

443761561344388063474665eta^4z+

82327155732241730770824eta z-

514623285385260545505123eta^2z-

1010535343560043404912120eta^2-

357788302700438191196160eta^5-

43808044579418934376632-

214023244873618345872240eta^4+

11818373349781028079eta^3+

347370177721463765064153eta$

}

\[2ex]

h(z)&=(417420z^2-4169121z-15571312)(1546z+3537)(3092z+17001)

end{align*}

\[2ex]

f(z)=frac{1}{382112640}frac{g(eta,z)}{h(z)}

end{gather*}



end{document}

I would use something like this

documentclass{article}

%usepackage{amsmath}% Loaded by mathtools

usepackage{mathtools}

begin{document}

Blah blah

[f(z)=frac{1}{382112640}cdotfrac{A}{B}]

where

begin{align*}

    A=&,-306772802511648469920eta^4z^4+762453974480763801600eta^5z^4\

    &,-1678626210368271790080eta^5z^3-28510918043555533736160eta^4z^3\

    &,+11443138641451067779872eta^3z^3-52164076923190540413504eta^2z^2\

    &,-78145258181161076156160eta^5z^2-211306163712129371808450eta^4z^2\

    &,+228927087397104405937944eta^3z^2+999881065017543109136462eta^3z\

    &,-317254092617698017425280eta^5z-443761561344388063474665eta^4z\

    &,+82327155732241730770824eta z-514623285385260545505123eta^2z\

    &,-1010535343560043404912120eta^2-357788302700438191196160eta^5\

    &,-43808044579418934376632-214023244873618345872240eta^4\

    &,+11818373349781028079eta^3+347370177721463765064153eta

end{align*}

and

[B=(417420z^2-4169121z-15571312)(1546z+3537)(3092z+17001)]

end{document}

or

documentclass{article}

%usepackage{amsmath}% Loaded by mathtools

usepackage{mathtools, nccmath}

begin{document}

    begin{multline*}medmath

f(z)=frac{1}{382112640}

    frac{left[

    begin{multlined}

    -306772802511648469920eta^4z^4+762453974480763801600eta^5z^4-\

    1678626210368271790080eta^5z^3-28510918043555533736160eta^4z^3+\

    11443138641451067779872eta^3z^3-52164076923190540413504eta^2z^2-\

    78145258181161076156160eta^5z^2-211306163712129371808450eta^4z^2+\

    228927087397104405937944eta^3z^2+999881065017543109136462eta^3z-\

    317254092617698017425280eta^5z-443761561344388063474665eta^4z+\

    82327155732241730770824eta z - 514623285385260545505123eta^2z-\

    1010535343560043404912120eta^2-357788302700438191196160eta^5-\

    43808044579418934376632-214023244873618345872240eta^4+\

    11818373349781028079eta^3+347370177721463765064153eta

    end{multlined}right]}

    {(417420z^2-4169121z-15571312)(1546z+3537)(3092z+17001)}

    end{multline*}

Given the nature of the operations, you can probably express this in a tidy manner using matrix multiplication notation, eg:

where:

Code:

$$ f(z)=frac{1}{382112640} frac{g(eta, z)}{u(z) , v(z) , w(z) } $$



where



$$

begin{array}{ll}

g(eta, z) = begin{bmatrix} 

begin{array}{r @{hspace{0em}} l}

- & 306772802511648469920 \

  & 762453974480763801600 \

- & 1678626210368271790080 \

- & 28510918043555533736160 \

 & 11443138641451067779872 \

- & 52164076923190540413504 \

- & 78145258181161076156160 \

- & 211306163712129371808450 \

 & 228927087397104405937944 \

 & 999881065017543109136462 \

- & 317254092617698017425280 \

- & 443761561344388063474665 \

 & 82327155732241730770824 \

- & 514623285385260545505123 \

- & 1010535343560043404912120 \

- & 357788302700438191196160 \

- & 43808044579418934376632 \

- & 214023244873618345872240 \

 & 11818373349781028079 \

 & 347370177721463765064153

end{array}

end{bmatrix}^T

begin{bmatrix}

eta^4z^4 \

eta^5z^4 \

eta^5z^3 \

eta^4z^3 \

eta^3z^3 \

eta^2z^2 \

eta^5z^2 \

eta^4z^2 \

eta^3z^2 \

eta^3z \

eta^5z \

eta^4z \

eta z \

eta^2z \

eta^2 \

eta^5 \

1 \

eta^4 \

eta^3 \

eta

end{bmatrix} & 

begin{array}{l}

u(z) = left ( begin{bmatrix} 417420 \ -4169121 \ -15571312 end{bmatrix}^T begin{bmatrix} z^2 \ z \ 1 end{bmatrix} right ) \[3em]

v(z) = left ( begin{bmatrix} 1546 \ 3537 end{bmatrix}^T begin{bmatrix} z \ 1 end{bmatrix} right ) \[3em]

w(z) = left ( begin{bmatrix} 3092 \ 17001end{bmatrix}^T begin{bmatrix} z \ 1 end{bmatrix} right ) \[3em]

end{array}

end{array}

$$

I recommend aligning the variables and adding some form of thousand-separators, both will enhance the readability. What I also recommend (but didn't do here) is sorting by the powers of the first and then the second variable. This is a modification of JuleV's answer.

documentclass{article}

%usepackage{amsmath}% Loaded by mathtools

usepackage{mathtools}

begin{document}

Blah blah

[f(z)=frac{1}{382112640}cdotfrac{A}{B}]

where

[

arraycolsep=0.5pt

begin{array}{rrllrll}

    A=&,      -306,772,802,511,648,469,920 &eta^4 &z^4 &      +762,453,974,480,763,801,600 &eta^5 &z^4\

    &,     -1,678,626,210,368,271,790,080 &eta^5 &z^3 &  -2,8510,918,043,555,533,736,160 &eta^4 &z^3\

    &,    +11,443,138,641,451,067,779,872 &eta^3 &z^3 &  -5,2164,076,923,190,540,413,504 &eta^2 &z^2\

    &,    -78,145,258,181,161,076,156,160 &eta^5 &z^2 & -21,1306,163,712,129,371,808,450 &eta^4 &z^2\

    &,   +228,927,087,397,104,405,937,944 &eta^3 &z^2 & +99,9881,065,017,543,109,136,462 &eta^3 &z\

    &,   -317,254,092,617,698,017,425,280 &eta^5 &z   & -44,3761,561,344,388,063,474,665 &eta^4 &z\

    &,    +82,327,155,732,241,730,770,824 &eta   &z   & -51,4623,285,385,260,545,505,123 &eta^2 &z\

    &,-1,010,535,343,560,043,404,912,120 &eta^2 &    & -35,7788,302,700,438,191,196,160 &eta^5 &\

    &,    -43,808,044,579,418,934,376,632 &       &    & -21,4023,244,873,618,345,872,240 &eta^4 &\

    &,         +11,818,373,349,781,028,079 &eta^3 &    & +34,7370,177,721,463,765,064,153 &eta   &

end{array}

]

and

[B=(417,420z^2-4,169,121z-15,571,312)(1,546z+3,537)(3,092z+17,001)]

end{document}

I'm sure there are also some custom packages that can do this for you but this is just using the packages you provided:

With the original disposition of the polynomial, but using alignat, parenthesis, and fractions to emphasize the different terms of the polynomial.

documentclass{article}



usepackage{mathtools}



begin{document}



begin{alignat*}{2}

& f(z) && = frac{1}{382112640} times left( vphantom{frac{1}{382112640}} -306772802511648469920 eta^4 z^4 + 762453974480763801600 eta^5 z^4 right. \[1.5ex] 

&  && -1678626210368271790080 eta^5 z^3 - 28510918043555533736160 eta^4 z^3 \[1.5ex]

&  && +11443138641451067779872 eta^3 z^3 -52164076923190540413504 eta^2 z^2 \[1.5ex]

&  && -78145258181161076156160 eta^5 z^2 -211306163712129371808450 eta^4 z^2 \[1.5ex]

&  && +228927087397104405937944 eta^3 z^2 +999881065017543109136462 eta^3 z \[1.5ex]

&  && -317254092617698017425280 eta^5 z -443761561344388063474665 eta^4 z \[1.5ex]

&  && +82327155732241730770824 eta z -514623285385260545505123 eta^2 z \[1.5ex]

&  && -1010535343560043404912120 eta^2 -357788302700438191196160 eta^5 \[1.5ex]

&  && -43808044579418934376632 - 214023244873618345872240 eta^4 \[1.5ex]

&  && +11818373349781028079 eta^3 +347370177721463765064153eta left. vphantom{frac{1}{382112640}} right) times frac{417420z^2-4169121z-15571312}{(1546z+3537)(3092z+17001)}

end{alignat*}

I would usually use the package breqn. That automatically line-breaks equations, and has a lot of very nice features, but uses low-level having into the maths primitives, which means it tends to make a mess of other packages what do the same thing (for example, you can't use both breqn and sansmath in the same document)

begin{dmath*}

f(z)=frac{1}{382112640}times-306772802511648469920eta^4z^4+left(762453974480763801600eta^5z^4-1678626210368271790080eta^5z^3-28510918043555533736160eta^4z^3+11443138641451067779872eta^3z^3-52164076923190540413504eta^2z^2-78145258181161076156160eta^5z^2-211306163712129371808450eta^4z^2+228927087397104405937944eta^3z^2+999881065017543109136462eta^3z-317254092617698017425280eta^5z-443761561344388063474665eta^4z+82327155732241730770824eta z-514623285385260545505123eta^2z-1010535343560043404912120eta^2-357788302700438191196160eta^5-43808044579418934376632-214023244873618345872240eta^4+11818373349781028079eta^3+347370177721463765064153etaright)timesleft(left(417420z^2-4169121z-15571312right)left(1546z+3537right)left(3092z+17001right)right)^{-1}

end{dmath*}

which produces

IMO the right-alignment is ugly but apparently that's the AMS standard - without the brackets it left aligns all those lines like the alginat version.