Let's simplify the equation step by step:

Expand the expression on the left side of the equation using the distributive property:

2(2x + 1)^2 - 8(x + 1)(x - 1) = 34
= 2(4x^2 + 4x + 1) - 8(x^2 - 1)
= 8x^2 + 8x + 2 - 8x^2 + 8
= 8x + 10

So, the simplified equation is: 8x + 10 = 34

Now, solve for x:

8x + 10 = 34
8x = 24
x = 3

Therefore, the solution to the equation is x = 3.