3m^2+12m=2m^2-20

Solution for 3m^2+12m=2m^2-20 equation:

Simplifying
3m2 + 12m = 2m2 + -20

Reorder the terms:
12m + 3m2 = 2m2 + -20

Reorder the terms:
12m + 3m2 = -20 + 2m2

Solving
12m + 3m2 = -20 + 2m2

Solving for variable 'm'.

Reorder the terms:
20 + 12m + 3m2 + -2m2 = -20 + 2m2 + 20 + -2m2

Combine like terms: 3m2 + -2m2 = 1m2
20 + 12m + 1m2 = -20 + 2m2 + 20 + -2m2

Reorder the terms:
20 + 12m + 1m2 = -20 + 20 + 2m2 + -2m2

Combine like terms: -20 + 20 = 0
20 + 12m + 1m2 = 0 + 2m2 + -2m2
20 + 12m + 1m2 = 2m2 + -2m2

Combine like terms: 2m2 + -2m2 = 0
20 + 12m + 1m2 = 0

Factor a trinomial.
(10 + m)(2 + m) = 0

Subproblem 1
Set the factor '(10 + m)' equal to zero and attempt to solve:

Simplifying
10 + m = 0

Solving
10 + m = 0

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

Add '-10' to each side of the equation.
10 + -10 + m = 0 + -10

Combine like terms: 10 + -10 = 0
0 + m = 0 + -10
m = 0 + -10

Combine like terms: 0 + -10 = -10
m = -10

Simplifying
m = -10
Subproblem 2
Set the factor '(2 + m)' equal to zero and attempt to solve:

Simplifying
2 + m = 0

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

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

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

Simplifying
m = -2
Solution
m = {-10, -2}