Answer
$x=\left\{ -\dfrac{2}{5},-1 \right\}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given eqution, $
(5x+2)(x+1)=0
,$ equate each factor to zero (Zero Product Property). Then solve each equation.
$\bf{\text{Solution Details:}}$
Equating each factor to zero (Zero Product Property), the solutions to the equation above are
\begin{array}{l}\require{cancel}
5x+2=0
\\\\\text{OR}\\\\
x+1=0
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
5x+2=0
\\\\
5x=-2
\\\\
x=-\dfrac{2}{5}
\\\\\text{OR}\\\\
x+1=0
\\\\
x=-1
.\end{array}
Hence, $
x=\left\{ -\dfrac{2}{5},-1 \right\}
.$