-n^2+9n-20=0

Solution for -n^2+9n-20=0 equation:

Simplifying
-1n2 + 9n + -20 = 0

Reorder the terms:
-20 + 9n + -1n2 = 0

Solving
-20 + 9n + -1n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-5 + n)(4 + -1n) = 0

Subproblem 1
Set the factor '(-5 + n)' equal to zero and attempt to solve:

Simplifying
-5 + n = 0

Solving
-5 + n = 0

Move all terms containing n to the left, all other terms to the right.

Add '5' to each side of the equation.
-5 + 5 + n = 0 + 5

Combine like terms: -5 + 5 = 0
0 + n = 0 + 5
n = 0 + 5

Combine like terms: 0 + 5 = 5
n = 5

Simplifying
n = 5
Subproblem 2
Set the factor '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

Solving
4 + -1n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -1n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1n = 0 + -4
-1n = 0 + -4

Combine like terms: 0 + -4 = -4
-1n = -4

Divide each side by '-1'.
n = 4

Simplifying
n = 4
Solution
n = {5, 4}