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

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

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

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

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

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

Combine like terms: -4m + 9m = 5m
(-6 + 5m + 6m2) = 0

Solving
-6 + 5m + 6m2 = 0

Solving for variable 'm'.

Factor a trinomial.
(-3 + -2m)(2 + -3m) = 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 '(2 + -3m)' equal to zero and attempt to solve:

Simplifying
2 + -3m = 0

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

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

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

Divide each side by '-3'.
m = 0.6666666667

Simplifying
m = 0.6666666667
Solution
m = {-1.5, 0.6666666667}