a^2+12a=-36

Solution for a^2+12a=-36 equation:

Simplifying
a2 + 12a = -36

Reorder the terms:
12a + a2 = -36

Solving
12a + a2 = -36

Solving for variable 'a'.

Reorder the terms:
36 + 12a + a2 = -36 + 36

Combine like terms: -36 + 36 = 0
36 + 12a + a2 = 0

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

Subproblem 1
Set the factor '(6 + a)' equal to zero and attempt to solve:

Simplifying
6 + a = 0

Solving
6 + a = 0

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

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

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

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

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

Simplifying
6 + a = 0

Solving
6 + a = 0

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

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

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

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

Simplifying
a = -6
Solution
a = {-6, -6}