## Intermediate Algebra (6th Edition)

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