C2 - Geometric series question

This question is from Edexcel C2 June 2015 Q5 (i)

It can be found here http://www.examsolutions.net/a-level-maths-papers/Edexcel/Core-Maths/Core-Maths-C2/2015-June/paper.php

I got 2 equations for a, by using the sum of the first n terms and sum to infinity, for geometric series':

a=162(1-r)

a=34(1-r)/(1-r^2)

I equated them, multiplied by the denominator and expanded to obtain

162-162r^2-162r+162r^3=34-34r

I cleaned this up to get

162r^3-162r^2-128r+128=0

From here I couldn't solve it... I plugged in the correct value for r and the equation is correct, but I don't see how this could be solved... Any ideas?

In red is serious overkill. Looks as if you just used the formula from the book.

Notice that 1-r is a factor in the numerator and denominator and so you can cancel.

Alternativly, sum of first two terms is a + ar = 34. So a = 34/(1+r)

Sorry I am confused... What is wrong with using the formula from the book, I thought that would be the sensible thing to do? And how is 1-r a factor in both? Surely (1-r) and (1-r^2) aren't the same thing? Unless you mean to use difference of two squares to convert 1-r^2 to (1+r)(1-r)