Answer
$x=\left\{ -1,-\dfrac{1}{2} \right\}$
Work Step by Step
The factored form of the given expression, $
(2x-1)(x+2)=-3
$, is
\begin{array}{}
2x^2+4x-x-2=-3
\\\\
2x^2+3x-2+3=0
\\\\
2x^2+3x+1=0
\\\\
(2x+1)(x+1)=0
.\end{array}
Equating each factor to zero, then
\begin{array}{l}
2x+1=0
\\
2x=0-1
\\
2x=-1
\\
x=-\dfrac{1}{2}
,\text{ OR}\\\\
x+1=0
\\
x=0-1
\\
x=-1
\end{array}
Hence, $
x=\left\{ -1,-\dfrac{1}{2} \right\}
$.
