a^2+18a+39=-6

Solution for a^2+18a+39=-6 equation:

Simplifying
a2 + 18a + 39 = -6

Reorder the terms:
39 + 18a + a2 = -6

Solving
39 + 18a + a2 = -6

Solving for variable 'a'.

Reorder the terms:
39 + 6 + 18a + a2 = -6 + 6

Combine like terms: 39 + 6 = 45
45 + 18a + a2 = -6 + 6

Combine like terms: -6 + 6 = 0
45 + 18a + a2 = 0

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

Subproblem 1
Set the factor '(15 + a)' equal to zero and attempt to solve:

Simplifying
15 + a = 0

Solving
15 + a = 0

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

Add '-15' to each side of the equation.
15 + -15 + a = 0 + -15

Combine like terms: 15 + -15 = 0
0 + a = 0 + -15
a = 0 + -15

Combine like terms: 0 + -15 = -15
a = -15

Simplifying
a = -15
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 = {-15, -3}