3m+12=2m^2-2m

Solution for 3m+12=2m^2-2m equation:

Simplifying
3m + 12 = 2m2 + -2m

Reorder the terms:
12 + 3m = 2m2 + -2m

Reorder the terms:
12 + 3m = -2m + 2m2

Solving
12 + 3m = -2m + 2m2

Solving for variable 'm'.

Combine like terms: 3m + 2m = 5m
12 + 5m + -2m2 = -2m + 2m2 + 2m + -2m2

Reorder the terms:
12 + 5m + -2m2 = -2m + 2m + 2m2 + -2m2

Combine like terms: -2m + 2m = 0
12 + 5m + -2m2 = 0 + 2m2 + -2m2
12 + 5m + -2m2 = 2m2 + -2m2

Combine like terms: 2m2 + -2m2 = 0
12 + 5m + -2m2 = 0

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

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 '(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 = {4, -1.5}