n^2+18n+72=0

Solution for n^2+18n+72=0 equation:

Simplifying
n2 + 18n + 72 = 0

Reorder the terms:
72 + 18n + n2 = 0

Solving
72 + 18n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(12 + n)(6 + n) = 0

Subproblem 1
Set the factor '(12 + n)' equal to zero and attempt to solve:

Simplifying
12 + n = 0

Solving
12 + n = 0

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

Add '-12' to each side of the equation.
12 + -12 + n = 0 + -12

Combine like terms: 12 + -12 = 0
0 + n = 0 + -12
n = 0 + -12

Combine like terms: 0 + -12 = -12
n = -12

Simplifying
n = -12
Subproblem 2
Set the factor '(6 + n)' equal to zero and attempt to solve:

Simplifying
6 + n = 0

Solving
6 + n = 0

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

Add '-6' to each side of the equation.
6 + -6 + n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + n = 0 + -6
n = 0 + -6

Combine like terms: 0 + -6 = -6
n = -6

Simplifying
n = -6
Solution
n = {-12, -6}