Answer
$x=45$
Work Step by Step
Using the properties of equality, the given equation, $
-\sqrt{3x+9}=-12
,$ is equivalent to
\begin{array}{l}\require{cancel}
\sqrt{3x+9}=12
.\end{array}
Squaring both sides of the equation above, then the solution/s is/are
\begin{array}{l}\require{cancel}
3x+9=144
\\\\
3x=144-9
\\\\
3x=135
\\\\
x=45
.\end{array}
Upon checking, only $
x=45
$ satisfies the original equation.