n^2+18n+65=0

Solution for n^2+18n+65=0 equation:

Simplifying
n2 + 18n + 65 = 0

Reorder the terms:
65 + 18n + n2 = 0

Solving
65 + 18n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(13 + n)(5 + n) = 0

Subproblem 1
Set the factor '(13 + n)' equal to zero and attempt to solve:

Simplifying
13 + n = 0

Solving
13 + n = 0

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

Add '-13' to each side of the equation.
13 + -13 + n = 0 + -13

Combine like terms: 13 + -13 = 0
0 + n = 0 + -13
n = 0 + -13

Combine like terms: 0 + -13 = -13
n = -13

Simplifying
n = -13
Subproblem 2
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
Solution
n = {-13, -5}