Answer
$x=\{ -2,0,2 \}$
Work Step by Step
Using factoring, the given equation, $
x^3=4x
$, is equivalent to
\begin{array}{l}\require{cancel}
x^3-4x=0
\\\\
x(x^2-4)=0
\\\\
x(x+2)(x-2)=0
.\end{array}
Equating each factor to $0$, then,
\begin{array}{l}\require{cancel}
x=0
,\\\\\text{OR}\\\\
x+2=0
\\\\
x=-2
,\\\\\text{OR}\\\\
x-2=0
\\\\
x=2
.\end{array}
Hence, $
x=\{ -2,0,2 \}
.$
