Help solving for $x$:$ 2^{2x+1 }- 5 \cdot2^{x} +2 = 0$

Question

Could someone please outline their steps in solving: $$2^{2x+1} -5\cdot2^x +2 = 0$$ The answer is $x = \pm1$, which I have found through trial and error, but I would like to find algebraically.

Answer 1

$$2^{2x+1} -5\cdot2^x +2 = 0$$

$$ 2^{2x}2^{1} - 5 \cdot 2^x + 2=0$$

Let $t=2^x$

$$ 2t^2-5t+2=0$$

$$ (2t-1)(t-2) =0$$

$$ t=\frac{1}{2} ,~~t=2$$

$$ 2^x=\frac{1}{2}=2^{-1} . ~~ 2^x=2 $$

$$ x=? , ~~ x=?$$