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