n^2+20n+96=0

Solution for n^2+20n+96=0 equation:

Simplifying
n2 + 20n + 96 = 0

Reorder the terms:
96 + 20n + n2 = 0

Solving
96 + 20n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(12 + n)(8 + 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 '(8 + n)' equal to zero and attempt to solve:

Simplifying
8 + n = 0

Solving
8 + n = 0

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

Add '-8' to each side of the equation.
8 + -8 + n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + n = 0 + -8
n = 0 + -8

Combine like terms: 0 + -8 = -8
n = -8

Simplifying
n = -8
Solution
n = {-12, -8}