k^2+12k=-27

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

Simplifying
k2 + 12k = -27

Reorder the terms:
12k + k2 = -27

Solving
12k + k2 = -27

Solving for variable 'k'.

Reorder the terms:
27 + 12k + k2 = -27 + 27

Combine like terms: -27 + 27 = 0
27 + 12k + k2 = 0

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

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

Simplifying
9 + k = 0

Solving
9 + k = 0

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

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

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

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

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

Simplifying
3 + k = 0

Solving
3 + k = 0

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

Add '-3' to each side of the equation.
3 + -3 + k = 0 + -3

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

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

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