Find all (real) solutions for $x$ in $ 2(2^x- 1) x^2 + (2^{x^2}-2)x = 2^{x+1} -2 . $

Question

Find all real solutions for $x$ in $$ 2(2^x- 1) x^2 + (2^{x^2}-2)x = 2^{x+1} -2 . $$

Expanding would be a bit messy, but I can't think of any other way. Thanks in advance!