Answer
$n=\left\{ -\dfrac{4}{9}, \dfrac{2}{9} \right\}$
Work Step by Step
Taking the square root of both sides, the solution/s of the given quadratic equation, $
(9n+1)^2=9
,$ is/are
\begin{array}{l}\require{cancel}
9n+1=\pm\sqrt{9}
\\\\
9n+1=\pm3
\\\\
9n=-1\pm3
\\\\
n=\dfrac{-1\pm3}{9}
\\\\
n=\left\{ -\dfrac{4}{9}, \dfrac{2}{9} \right\}
.\end{array}
