3m^2+15m+12=0

Solution for 3m^2+15m+12=0 equation:

Simplifying
3m2 + 15m + 12 = 0

Reorder the terms:
12 + 15m + 3m2 = 0

Solving
12 + 15m + 3m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + 5m + m2) = 0

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

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

Simplifying
4 + m = 0

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

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

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

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

Simplifying
1 + m = 0

Solving
1 + m = 0

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

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

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

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

Simplifying
m = -1
Solution
m = {-4, -1}