Answer
$x=\left\{ -3 \right\}$
Work Step by Step
Factoring the given equation, $
0=6x+x^2+9
,$ results to
\begin{array}{l}\require{cancel}
6x+x^2+9=0
\\\\
x^2+6x+9=0
\\\\
(x+3)^2=0
\\\\
(x+3)(x+3)=0
.\end{array}
Equating each factor to zero (Zero Product Principle), then the solutions to the equation, $
(x+3)(x+3)=0
,$ are
\begin{array}{l}\require{cancel}
x+3=0
\\\\
x=-3
,\\\\\text{OR}\\\\
x+3=0
\\\\
x=-3
.\end{array}
Hence, $
x=\left\{ -3 \right\}
.$