Answer
$x=\left\{ -\dfrac{2}{3},6 \right\}$
Work Step by Step
The factored form of the given equation, $
3x^2=16x+12
,$ is
\begin{align*}
3x^2&=16x+12
\\
3x^2-16x-12&=0
\\
(3x+2)(x-6)&=0
.\end{align*}
Equating each factor to zero (Zero Product Property), the solutions of the equation above are
\begin{align*}
3x+2&=0
\\\\\text{ OR}\\\\
x-6&=0
.\end{align*}
Solving each equation above results to
\begin{align*}
3x+2&=0
\\
3x&=-2
\\
\dfrac{3x}{3}&=-\dfrac{2}{3}
\\
x&=-\dfrac{2}{3}
\\\\\text{ OR}\\\\
x-6&=0
\\
x&=6
.\end{align*}
Hence, the solutions are $
x=\left\{ -\dfrac{2}{3},6 \right\}
.$
