Answer
$x=\left\{ -2,\dfrac{7}{2} \right\}$
Work Step by Step
The factored form of the given expression, $
2x^2-3x-14=0
,$ is
\begin{align*}
(2x-7)(x+2)&=0
.\end{align*}
Equating each factor to zero (Zero Product Property), then
\begin{align*}
2x-7&=0
\\\\\text{ OR }\\\\
x+2&=0
.\end{align*}
Solving each of the equations above results to
\begin{align*}
2x-7&=0
\\
2x&=7
\\
\dfrac{2x}{2}&=\dfrac{7}{2}
\\
x&=\dfrac{7}{2}
\\\\\text{ OR }\\\\
x+2&=0
\\
x&=-2
.\end{align*}
Hence, the solutions are $
x=\left\{ -2,\dfrac{7}{2} \right\}
.$
