#### Answer

$n=-\dfrac{5}{3}$

#### Work Step by Step

The factored form of the given expression, $
9n^2+30n+25=0
$, is
\begin{array}{}
(3n+5)(3n+5)=0
\\\\
(3n+5)^2=0
.\end{array}
Taking the square root of both sides, then,
\begin{array}{l}
3n+5=\pm\sqrt{0}
\\\\
3n+5=0
\\\\
3n=0-5
\\\\
3n=-5
\\\\
n=-\dfrac{5}{3}
\end{array}