Answer
$x=\left\{ -\dfrac{1}{3},0 \right\}$
Work Step by Step
The factored form of the given expression, $
3x^2=-x
$, is
\begin{array}{l}
3x^2+x=0
\\\\
x(3x+1)=0
.\end{array}
Equating each factor to zero, then
\begin{array}{l}
x=0
,\text{ OR}\\\\
3x+1=0
\\
3x=0-1
\\
3x=-1
\\
x=-\dfrac{1}{3}
.\end{array}
Hence, $
x=\left\{ -\dfrac{1}{3},0 \right\}
$.
