Answer
$n=3, 7/2$
Work Step by Step
$(2n-3)^2-7(2n-3)+12=0$
$2n-3=x$
$(2n-3)^2-7(2n-3)+12=0$
$x^2-7x+12=0$
$(x-4)(x-3)=0$
$(2n-3-4)(2n-3-3)=0$
$(2n-7)(2n-6)=0$
$2n-7=0$
$2n=7$
$2n/2=7/2$
$n=7/2$
$2n-6=0$
$2n=6$
$2n/2=6/2$
$n=3$