(m^2+6m+9)+(2m+6)=0

Solution for (m^2+6m+9)+(2m+6)=0 equation:

Simplifying
(m2 + 6m + 9) + (2m + 6) = 0

Reorder the terms:
(9 + 6m + m2) + (2m + 6) = 0

Remove parenthesis around (9 + 6m + m2)
9 + 6m + m2 + (2m + 6) = 0

Reorder the terms:
9 + 6m + m2 + (6 + 2m) = 0

Remove parenthesis around (6 + 2m)
9 + 6m + m2 + 6 + 2m = 0

Reorder the terms:
9 + 6 + 6m + 2m + m2 = 0

Combine like terms: 9 + 6 = 15
15 + 6m + 2m + m2 = 0

Combine like terms: 6m + 2m = 8m
15 + 8m + m2 = 0

Solving
15 + 8m + m2 = 0

Solving for variable 'm'.

Factor a trinomial.
(5 + m)(3 + m) = 0

Subproblem 1
Set the factor '(5 + m)' equal to zero and attempt to solve:

Simplifying
5 + m = 0

Solving
5 + m = 0

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

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

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

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

Simplifying
m = -5
Subproblem 2
Set the factor '(3 + m)' equal to zero and attempt to solve:

Simplifying
3 + m = 0

Solving
3 + m = 0

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

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

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

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

Simplifying
m = -3
Solution
m = {-5, -3}