Answer
$x=\left\{ -\dfrac{2}{3},0 \right\}$
Work Step by Step
The factored form of the given equation, $
6x^2+4x=0
,$ is
\begin{align*}
2x(3x+2)=0
.\end{align*}
Equating each factor to zero (Zero Product Property), the solutions of the equation above are
\begin{align*}
2x&=0
\\\\\text{ OR}\\\\
3x+2&=0
.\end{align*}
Solving each equation above results to
\begin{align*}
2x&=0
\\
\dfrac{2x}{2}&=\dfrac{0}{2}
\\
x&=0
\\\\\text{ OR}\\\\
3x+2&=0
\\
3x&=-2
\\
\dfrac{3x}{3}&=-\dfrac{2}{3}
\\
x&=-\dfrac{2}{3}
.\end{align*}
Hence, the solutions are $
x=\left\{ -\dfrac{2}{3},0 \right\}
.$
