Answer
$n=-4/5, 0$
Work Step by Step
$(5n+1)^2+2(5n+1)-3=0$
$x=5n+1$
$(5n+1)^2+2(5n+1)-3=0$
$x^2+2x-3=0$
$(x+3)(x-1)=0$
$x+3=0$
$x=-3$
$x-1=0$
$x=1$
$-3=5n+1$
$-4=5n$
$-4/5=5n/5$
$-4/5=n$
$1=5n+1$
$0=5n$
$0/5=5n/5$
$n=0$