Solve the equation for n

Question

n!/(n-2)! = 90
I get n= 10 but when i plug 10 back into the equation i don't get 90 to check...
My work:
n!/(n-2)! =90
n(n-1)(n-2)/(n-2)! =90 i cancelled the n-2 and expanded the n(n-1)
n^2 -1n -90 =0
(n-10)(n+9) = 0

Answer 1

n * (n-1) = 90 the rest cancels agree

n^2 - n = 90

n^2 - n - 90 = 0 agree

n = 10 or n = -9 agree

10 * 9 [ (n-2)! / (n-2)! ] = 90
for me all right