Answer
$x=-6$
Work Step by Step
Using the properties of equality, the given equation, $
\sqrt[3]{6x+9}+5=2
$, is equivalent to
\begin{array}{l}
\sqrt[3]{6x+9}=2-5
\\\\
\sqrt[3]{6x+9}=-3
.\end{array}
Raising both sides to the $\text{
3rd
}$ power, the solution to the equation above, $
\sqrt[3]{6x+9}=-3
$, is
\begin{array}{l}
6x+9=-27
\\\\
6x=-27-9
\\\\
6x=-36
\\\\
x=-\dfrac{36}{6}
\\\\
x=-6
.\end{array}
