5(n^2-8n+15)=0

Solution for 5(n^2-8n+15)=0 equation:

Simplifying
5(n2 + -8n + 15) = 0

Reorder the terms:
5(15 + -8n + n2) = 0
(15 * 5 + -8n * 5 + n2 * 5) = 0
(75 + -40n + 5n2) = 0

Solving
75 + -40n + 5n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '5'.
5(15 + -8n + n2) = 0

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

Ignore the factor 5.
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}