8n^2-64n+120=0

Solution for 8n^2-64n+120=0 equation:

Simplifying
8n2 + -64n + 120 = 0

Reorder the terms:
120 + -64n + 8n2 = 0

Solving
120 + -64n + 8n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '8'.
8(15 + -8n + n2) = 0

Factor a trinomial.
8((3 + -1n)(5 + -1n)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

Solving
5 + -1n = 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 + -1n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1n = 0 + -5
-1n = 0 + -5

Combine like terms: 0 + -5 = -5
-1n = -5

Divide each side by '-1'.
n = 5

Simplifying
n = 5
Solution
n = {3, 5}