Exponential Equation with quadratic variable as an exponent

Question

How to solve this exponential equation $$2^{2x^2} + 2^{x^2+2x+2}= 2^{5+4x}$$

Answer 1

HINT:

$$(2{x^2})^2+2^{x^2}\cdot2^{2x+2}-2\cdot(2^{2x+2})^2=0$$

$$\iff\left(2^{x^2-2x-2}\right)^2+2^{x^2-2x-2}-2=0$$