6m(m-2)=3(2-m)

Solution for 6m(m-2)=3(2-m) equation:

Simplifying
6m(m + -2) = 3(2 + -1m)

Reorder the terms:
6m(-2 + m) = 3(2 + -1m)
(-2 * 6m + m * 6m) = 3(2 + -1m)
(-12m + 6m2) = 3(2 + -1m)
-12m + 6m2 = (2 * 3 + -1m * 3)
-12m + 6m2 = (6 + -3m)

Solving
-12m + 6m2 = 6 + -3m

Solving for variable 'm'.

Reorder the terms:
-6 + -12m + 3m + 6m2 = 6 + -3m + -6 + 3m

Combine like terms: -12m + 3m = -9m
-6 + -9m + 6m2 = 6 + -3m + -6 + 3m

Reorder the terms:
-6 + -9m + 6m2 = 6 + -6 + -3m + 3m

Combine like terms: 6 + -6 = 0
-6 + -9m + 6m2 = 0 + -3m + 3m
-6 + -9m + 6m2 = -3m + 3m

Combine like terms: -3m + 3m = 0
-6 + -9m + 6m2 = 0

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

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

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + -2m)' equal to zero and attempt to solve:

Simplifying
-1 + -2m = 0

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

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

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

Divide each side by '-2'.
m = -0.5

Simplifying
m = -0.5
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 = {-0.5, 2}