Answer
$x=\{ -7,0 \}$
Work Step by Step
Factoring out the $GCF=
x
,$ the factored form of the given expression, $
x^2+7x=0
,$ is
\begin{array}{l}\require{cancel}
x(x+7)
=0
.\end{array}
Equating each factor to zero, wo obtain:
\begin{array}{l}\require{cancel}
x=0
,\\\\\text{OR}\\\\
x+7=0
\\\\
x=-7
.\end{array}
Hence, the solution set is $
x=\{ -7,0 \}
.$
