(m-2)(3m+12)=0

Solution for (m-2)(3m+12)=0 equation:

Simplifying
(m + -2)(3m + 12) = 0

Reorder the terms:
(-2 + m)(3m + 12) = 0

Reorder the terms:
(-2 + m)(12 + 3m) = 0

Multiply (-2 + m) * (12 + 3m)
(-2(12 + 3m) + m(12 + 3m)) = 0
((12 * -2 + 3m * -2) + m(12 + 3m)) = 0
((-24 + -6m) + m(12 + 3m)) = 0
(-24 + -6m + (12 * m + 3m * m)) = 0
(-24 + -6m + (12m + 3m2)) = 0

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

Solving
-24 + 6m + 3m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + 2m + m2) = 0

Factor a trinomial.
3((-4 + -1m)(2 + -1m)) = 0

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

Simplifying
-4 + -1m = 0

Solving
-4 + -1m = 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 + -1m = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1m = 0 + 4
-1m = 0 + 4

Combine like terms: 0 + 4 = 4
-1m = 4

Divide each side by '-1'.
m = -4

Simplifying
m = -4
Subproblem 2
Set the factor '(2 + -1m)' equal to zero and attempt to solve:

Simplifying
2 + -1m = 0

Solving
2 + -1m = 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 + -1m = 0 + -2

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

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

Divide each side by '-1'.
m = 2

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