Answer
$x=\left\{ -1,0,1 \right\}$
Work Step by Step
Factoring the equation and then equating each factor to zero (Zero-Product Property), then the values of $x$ that satisfy the given equation, $
x^3=x
,$ are
\begin{array}{l}\require{cancel}
x^3-x=0
\\\\
x(x^2-1)=0
\\\\
x(x+1)(x-1)=0
\\\\
x=0
,\\\\\text{OR}\\\\
x+1=0
\\\\
x=-1
,\\\\\text{OR}\\\\
x-1=0
\\\\
x=1
.\end{array}
Hence, $
x=\left\{ -1,0,1 \right\}
.$
