(4m+2)(3m+9)=0

Solution for (4m+2)(3m+9)=0 equation:

Simplifying
(4m + 2)(3m + 9) = 0

Reorder the terms:
(2 + 4m)(3m + 9) = 0

Reorder the terms:
(2 + 4m)(9 + 3m) = 0

Multiply (2 + 4m) * (9 + 3m)
(2(9 + 3m) + 4m * (9 + 3m)) = 0
((9 * 2 + 3m * 2) + 4m * (9 + 3m)) = 0
((18 + 6m) + 4m * (9 + 3m)) = 0
(18 + 6m + (9 * 4m + 3m * 4m)) = 0
(18 + 6m + (36m + 12m2)) = 0

Combine like terms: 6m + 36m = 42m
(18 + 42m + 12m2) = 0

Solving
18 + 42m + 12m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '6'.
6(3 + 7m + 2m2) = 0

Factor a trinomial.
6((3 + m)(1 + 2m)) = 0

Ignore the factor 6.
Subproblem 1
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
Subproblem 2
Set the factor '(1 + 2m)' equal to zero and attempt to solve:

Simplifying
1 + 2m = 0

Solving
1 + 2m = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2m = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2m = 0 + -1
2m = 0 + -1

Combine like terms: 0 + -1 = -1
2m = -1

Divide each side by '2'.
m = -0.5

Simplifying
m = -0.5
Solution
m = {-3, -0.5}