a^2+12a=-27

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

Simplifying
a2 + 12a = -27

Reorder the terms:
12a + a2 = -27

Solving
12a + a2 = -27

Solving for variable 'a'.

Reorder the terms:
27 + 12a + a2 = -27 + 27

Combine like terms: -27 + 27 = 0
27 + 12a + a2 = 0

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

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

Simplifying
9 + a = 0

Solving
9 + a = 0

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

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

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

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

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

Simplifying
3 + a = 0

Solving
3 + a = 0

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

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

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

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

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