(m+4)(3m+6)=0

Solution for (m+4)(3m+6)=0 equation:

Simplifying
(m + 4)(3m + 6) = 0

Reorder the terms:
(4 + m)(3m + 6) = 0

Reorder the terms:
(4 + m)(6 + 3m) = 0

Multiply (4 + m) * (6 + 3m)
(4(6 + 3m) + m(6 + 3m)) = 0
((6 * 4 + 3m * 4) + m(6 + 3m)) = 0
((24 + 12m) + m(6 + 3m)) = 0
(24 + 12m + (6 * m + 3m * m)) = 0
(24 + 12m + (6m + 3m2)) = 0

Combine like terms: 12m + 6m = 18m
(24 + 18m + 3m2) = 0

Solving
24 + 18m + 3m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '3'.
3(8 + 6m + m2) = 0

Factor a trinomial.
3((4 + m)(2 + m)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(4 + m)' equal to zero and attempt to solve:

Simplifying
4 + m = 0

Solving
4 + m = 0

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

Add '-4' to each side of the equation.
4 + -4 + m = 0 + -4

Combine like terms: 4 + -4 = 0
0 + m = 0 + -4
m = 0 + -4

Combine like terms: 0 + -4 = -4
m = -4

Simplifying
m = -4
Subproblem 2
Set the factor '(2 + m)' equal to zero and attempt to solve:

Simplifying
2 + m = 0

Solving
2 + m = 0

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

Add '-2' to each side of the equation.
2 + -2 + m = 0 + -2

Combine like terms: 2 + -2 = 0
0 + m = 0 + -2
m = 0 + -2

Combine like terms: 0 + -2 = -2
m = -2

Simplifying
m = -2
Solution
m = {-4, -2}