n^2+12n=-27

Solution for n^2+12n=-27 equation:

Simplifying
n2 + 12n = -27

Reorder the terms:
12n + n2 = -27

Solving
12n + n2 = -27

Solving for variable 'n'.

Reorder the terms:
27 + 12n + n2 = -27 + 27

Combine like terms: -27 + 27 = 0
27 + 12n + n2 = 0

Factor a trinomial.
(9 + n)(3 + n) = 0

Subproblem 1
Set the factor '(9 + n)' equal to zero and attempt to solve:

Simplifying
9 + n = 0

Solving
9 + n = 0

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

Add '-9' to each side of the equation.
9 + -9 + n = 0 + -9

Combine like terms: 9 + -9 = 0
0 + n = 0 + -9
n = 0 + -9

Combine like terms: 0 + -9 = -9
n = -9

Simplifying
n = -9
Subproblem 2
Set the factor '(3 + n)' equal to zero and attempt to solve:

Simplifying
3 + n = 0

Solving
3 + n = 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 + n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + n = 0 + -3
n = 0 + -3

Combine like terms: 0 + -3 = -3
n = -3

Simplifying
n = -3
Solution
n = {-9, -3}