a^2+12a+29=-6

Solution for a^2+12a+29=-6 equation:

Simplifying
a2 + 12a + 29 = -6

Reorder the terms:
29 + 12a + a2 = -6

Solving
29 + 12a + a2 = -6

Solving for variable 'a'.

Reorder the terms:
29 + 6 + 12a + a2 = -6 + 6

Combine like terms: 29 + 6 = 35
35 + 12a + a2 = -6 + 6

Combine like terms: -6 + 6 = 0
35 + 12a + a2 = 0

Factor a trinomial.
(7 + a)(5 + a) = 0

Subproblem 1
Set the factor '(7 + a)' equal to zero and attempt to solve:

Simplifying
7 + a = 0

Solving
7 + a = 0

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

Add '-7' to each side of the equation.
7 + -7 + a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + a = 0 + -7
a = 0 + -7

Combine like terms: 0 + -7 = -7
a = -7

Simplifying
a = -7
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 = {-7, -5}