Answer
$x=\left\{ -2,-1 \right\}$
Work Step by Step
The factored form of the given equation, $
2x^2+6x=-4
,$ is
\begin{align*}
2x^2+6x+4&=0
\\
2(x^2+3x+2)&=0
\\\\
\dfrac{2(x^2+3x+2)}{2}&=\dfrac{0}{2}
\\\\
x^2+3x+2&=0
\\
(x+2)(x+1)&=0
.\end{align*}
Equating each factor to zero (Zero Product Property), the solutions of the equation above are
\begin{align*}
x+2&=0
\\\\\text{ OR}\\\\
x+1&=0
.\end{align*}
Solving each equation above results to
\begin{align*}
x+2&=0
\\
x&=-2
\\\\\text{ OR}\\\\
x+1&=0
\\
x&=-1
.\end{align*}
Hence, the solutions are $
x=\left\{ -2,-1 \right\}
.$
