math help.... assignment..?

Question

can you please find the roots of this equation.. thanks.. pease include the step by step solution....

180^2 (y^2 + 4y + 69)^3 = 100^2 (y^2 - 8y + 29)^3

Answer 1

This may be a bit of Heath-Robinson solution, but in the absence of other answers maybe it will help.

6 degree equation so there may be 6 complex roots .. do you just want real roots?
Graphing in excel suggests there is one root near y= -6.8864

i don't remember solution of cubics, but this should simplify

let u = y^2+49
and v = 4y +20
and z = u/v

81(u+v)^3=25(u-2v)^3
81( u^3+3u^2v+3uv^2+v^3)=25(u^3-6u^2v+12uv^2-8v^3)
56u^3+393 u^2v-57uv^2+281v^3=0
56 z^3 + 393 z^2 -57 z +281 =0

Again I think there is one real root. Find it.
Then backsubsitute
y^2+49 = [that root] (4y+20)
and solve that quadratic