Chapter 5 - Section 5.8 - Solving Equations by Factoring and Problem Solving - Exercise Set - Page 323: 40

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

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}