Find all real solutions for $x$ in $$ 2(2^x- 1) x^2 + (2^{x^2}-2)x = 2^{x+1} -2 . $$
I tried doing this problem and simplified it all the way to $x^2 + \frac{(2^{x^2-1} - 1)x}{2^x - 1}=1$.(sorry if you don't know latex) but I can't figure it out from here, help?
