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

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

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

Reorder the terms:
6 + -2m + -3m(-3 + m) = (6 + -2m) + -3m
6 + -2m + (-3 * -3m + m * -3m) = (6 + -2m) + -3m
6 + -2m + (9m + -3m2) = (6 + -2m) + -3m

Combine like terms: -2m + 9m = 7m
6 + 7m + -3m2 = (6 + -2m) + -3m

Remove parenthesis around (6 + -2m)
6 + 7m + -3m2 = 6 + -2m + -3m

Combine like terms: -2m + -3m = -5m
6 + 7m + -3m2 = 6 + -5m

Add '-6' to each side of the equation.
6 + 7m + -6 + -3m2 = 6 + -6 + -5m

Reorder the terms:
6 + -6 + 7m + -3m2 = 6 + -6 + -5m

Combine like terms: 6 + -6 = 0
0 + 7m + -3m2 = 6 + -6 + -5m
7m + -3m2 = 6 + -6 + -5m

Combine like terms: 6 + -6 = 0
7m + -3m2 = 0 + -5m
7m + -3m2 = -5m

Solving
7m + -3m2 = -5m

Solving for variable 'm'.

Reorder the terms:
7m + 5m + -3m2 = -5m + 5m

Combine like terms: 7m + 5m = 12m
12m + -3m2 = -5m + 5m

Combine like terms: -5m + 5m = 0
12m + -3m2 = 0

Factor out the Greatest Common Factor (GCF), '3m'.
3m(4 + -1m) = 0

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

Simplifying
m = 0

Solving
m = 0

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

Simplifying
m = 0
Subproblem 2
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
Solution
m = {0, 4}