Calculate: x^3=16x

Expression: ${x}^{3}=16x$

Move the variable to the left-hand side and change its sign

${x}^{3}-16x=0$

Factor out $x$ from the expression

$x \times \left( {x}^{2}-16 \right)=0$

When the product of factors equals $0$, at least one factor is $0$

$\begin{array} { l }x=0,\\{x}^{2}-16=0\end{array}$

Solve the equation for $x$

$\begin{array} { l }x=0,\\x=-4,\\x=4\end{array}$

The equation has $3$ solutions

$\begin{array} { l }x_1=-4,& x_2=0,& x_3=4\end{array}$