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

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

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

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

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

Multiply (-3 + 2m) * (9 + 3m)
(-3(9 + 3m) + 2m * (9 + 3m)) = 0
((9 * -3 + 3m * -3) + 2m * (9 + 3m)) = 0
((-27 + -9m) + 2m * (9 + 3m)) = 0
(-27 + -9m + (9 * 2m + 3m * 2m)) = 0
(-27 + -9m + (18m + 6m2)) = 0

Combine like terms: -9m + 18m = 9m
(-27 + 9m + 6m2) = 0

Solving
-27 + 9m + 6m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-9 + 3m + 2m2) = 0

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

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

Simplifying
-3 + -1m = 0

Solving
-3 + -1m = 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 + -1m = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1m = 0 + 3
-1m = 0 + 3

Combine like terms: 0 + 3 = 3
-1m = 3

Divide each side by '-1'.
m = -3

Simplifying
m = -3
Subproblem 2
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
Solution
m = {-3, 1.5}