Answer
$x=\left\{ -\dfrac{1}{3}, 0, 3 \right\}$
Work Step by Step
Equating each factor to zero (or the Zero-Product Principle), then the solutions to the given equation, $
2x(3x+1)(x-3)=0
,$ is
\begin{array}{l}\require{cancel}
2x=0
\\\\
x=\dfrac{0}{2}
\\\\
x=0
,\\\\\text{OR}\\\\
3x+1=0
\\\\
3x=-1
\\\\
x=-\dfrac{1}{3}
,\\\\\text{OR}\\\\
x-3=0
\\\\
x=3
.\end{array}
Hence, $
x=\left\{ -\dfrac{1}{3}, 0, 3 \right\}
.$
