How do I find the power x in this equation?

Question

How do I find $x$ in this $$2^{2x} + 2^x+2 = 2^4\ ?$$ Any help would be much appreciated.

Answer 1

Use the changement of variable $y=2^x$.

Then you end up with

$$y^2+y+2=2^4=16$$

so

$$y^2+y-14=0.$$

I think you can take it from here.