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

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

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

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

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

Multiply (3 + 2m) * (3 + 4m)
(3(3 + 4m) + 2m * (3 + 4m)) = 0
((3 * 3 + 4m * 3) + 2m * (3 + 4m)) = 0
((9 + 12m) + 2m * (3 + 4m)) = 0
(9 + 12m + (3 * 2m + 4m * 2m)) = 0
(9 + 12m + (6m + 8m2)) = 0

Combine like terms: 12m + 6m = 18m
(9 + 18m + 8m2) = 0

Solving
9 + 18m + 8m2 = 0

Solving for variable 'm'.

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

Subproblem 1
Set the factor '(3 + 2m)' equal to zero and attempt to solve:

Simplifying
3 + 2m = 0

Solving
3 + 2m = 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 + 2m = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2m = 0 + -3
2m = 0 + -3

Combine like terms: 0 + -3 = -3
2m = -3

Divide each side by '2'.
m = -1.5

Simplifying
m = -1.5
Subproblem 2
Set the factor '(3 + 4m)' equal to zero and attempt to solve:

Simplifying
3 + 4m = 0

Solving
3 + 4m = 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 + 4m = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4m = 0 + -3
4m = 0 + -3

Combine like terms: 0 + -3 = -3
4m = -3

Divide each side by '4'.
m = -0.75

Simplifying
m = -0.75
Solution
m = {-1.5, -0.75}