#### Answer

$n=0$ and $n=-\frac{4}{5}$

#### Work Step by Step

Let
$u=5n+1$
Rewrite the given equation using the variable $u$ to obtain:
$u^2+2u-3=0$
Factor the trinomial to obtain:
$(u+3)(u-1)=0$
Use the Zero-Factor Property by equating each unique factor to zero. then solve:
$u+3 = 0 \text{ or } u-1=0
\\u=-3 \text{ or } u=1$
Since $u=5n+1$, then
\begin{array}{ccc}
&u= -3 &\text{or} &u=1
\\&5n+1=-3 &\text{or} &5n+1=1
\\&5n=-3-1 &\text{or} &5n=1-1
\\&5n=-4 &\text{or} &5n=0
\\&n=-\frac{4}{5} &\text{or} &n=0\end{array}
Thus, the solutions are $n=0$ and $n=-\frac{4}{5}$.