a^2+14a+39=-6

Solution for a^2+14a+39=-6 equation:

Simplifying
a2 + 14a + 39 = -6

Reorder the terms:
39 + 14a + a2 = -6

Solving
39 + 14a + a2 = -6

Solving for variable 'a'.

Reorder the terms:
39 + 6 + 14a + a2 = -6 + 6

Combine like terms: 39 + 6 = 45
45 + 14a + a2 = -6 + 6

Combine like terms: -6 + 6 = 0
45 + 14a + a2 = 0

Factor a trinomial.
(9 + a)(5 + 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 '(5 + a)' equal to zero and attempt to solve:

Simplifying
5 + a = 0

Solving
5 + a = 0

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

Add '-5' to each side of the equation.
5 + -5 + a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + a = 0 + -5
a = 0 + -5

Combine like terms: 0 + -5 = -5
a = -5

Simplifying
a = -5
Solution
a = {-9, -5}