n^2-19n+65=5

Solution for n^2-19n+65=5 equation:

Simplifying
n2 + -19n + 65 = 5

Reorder the terms:
65 + -19n + n2 = 5

Solving
65 + -19n + n2 = 5

Solving for variable 'n'.

Reorder the terms:
65 + -5 + -19n + n2 = 5 + -5

Combine like terms: 65 + -5 = 60
60 + -19n + n2 = 5 + -5

Combine like terms: 5 + -5 = 0
60 + -19n + n2 = 0

Factor a trinomial.
(4 + -1n)(15 + -1n) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(15 + -1n)' equal to zero and attempt to solve:

Simplifying
15 + -1n = 0

Solving
15 + -1n = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1n = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1n = 0 + -15
-1n = 0 + -15

Combine like terms: 0 + -15 = -15
-1n = -15

Divide each side by '-1'.
n = 15

Simplifying
n = 15
Solution
n = {4, 15}