(4m+12)(3m-15)=0

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Solution for (4m+12)(3m-15)=0 equation: 


Simplifying
(4m + 12)(3m + -15) = 0

Reorder the terms:
(12 + 4m)(3m + -15) = 0

Reorder the terms:
(12 + 4m)(-15 + 3m) = 0

Multiply (12 + 4m) * (-15 + 3m)
(12(-15 + 3m) + 4m * (-15 + 3m)) = 0
((-15 * 12 + 3m * 12) + 4m * (-15 + 3m)) = 0
((-180 + 36m) + 4m * (-15 + 3m)) = 0
(-180 + 36m + (-15 * 4m + 3m * 4m)) = 0
(-180 + 36m + (-60m + 12m2)) = 0

Combine like terms: 36m + -60m = -24m
(-180 + -24m + 12m2) = 0

Solving
-180 + -24m + 12m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-15 + -2m + m2) = 0

Factor a trinomial.
12((-3 + -1m)(5 + -1m)) = 0

Ignore the factor 12.

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 '(5 + -1m)' equal to zero and attempt to solve:

Simplifying
5 + -1m = 0

Solving
5 + -1m = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1m = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1m = 0 + -5
-1m = 0 + -5

Combine like terms: 0 + -5 = -5
-1m = -5

Divide each side by '-1'.
m = 5

Simplifying
m = 5
Solution
m = {-3, 5}

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