Hello,

This is correct9 (1-q)^8 q = 36 (1-q)^7 q^2

Now, divide both sides by (1-q)^7 and by 9q.

I explain why :

this is equivalent to :

(9(1-q)^8 q)-(36(1-q)^7 q^2)=0

Factor out the common factors (q^2=q*q, 36=4*9, (1-q)^8=(1-q)^7*q)

Then, solve