# Solve for: 2^{2x}+2^{x+2}-4 * 2^3=0

## Expression: ${2}^{2x}+{2}^{x+2}-4 \times {2}^{3}=0$

Use ${a}^{mn}={\left( {a}^{n} \right)}^{m}$ to transform the expression

${\left( {2}^{x} \right)}^{2}+{2}^{x+2}-4 \times {2}^{3}=0$

Use ${a}^{m+n}={a}^{m} \times {a}^{n}$ to expand the expression

${\left( {2}^{x} \right)}^{2}+{2}^{x} \times {2}^{2}-4 \times {2}^{3}=0$

Evaluate the power

${\left( {2}^{x} \right)}^{2}+{2}^{x} \times {2}^{2}-4 \times 8=0$

Evaluate the power

${\left( {2}^{x} \right)}^{2}+{2}^{x} \times 4-4 \times 8=0$

Multiply the numbers

${\left( {2}^{x} \right)}^{2}+{2}^{x} \times 4-32=0$

To get an equation that is easier to solve, substitute $t$ for ${2}^{x}$

${t}^{2}+t \times 4-32=0$

Solve the equation for $t$

$\begin{array} { l }t=-8,\\t=4\end{array}$

Substitute back $t={2}^{x}$

$\begin{array} { l }{2}^{x}=-8,\\{2}^{x}=4\end{array}$

Solve the equation for $x$

$\begin{array} { l }x\notin ℝ,\\{2}^{x}=4\end{array}$

Solve the equation for $x$

$\begin{array} { l }x\notin ℝ,\\x=2\end{array}$

Find the union

$x=2$

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