Factorial Simplification

(n-1)!(n^2+n)
= (n-1)!(n)(n+1)
= (n+1)!

(n!)/(n-2)!
(n)(n-1)(n-2)! / (n-2)!
(n)(n-1)
n^2 - n - 20 = 0
quadratic formula: n=5,-4
n != -4. cannot negative factorial
n = 5