6m(m-1)=3(1-m)

Solution for 6m(m-1)=3(1-m) equation:

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

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

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

Solving for variable 'm'.

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + -1m + 2m2) = 0

Factor a trinomial.
3((-1 + -2m)(1 + -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 '(1 + -1m)' equal to zero and attempt to solve:

Simplifying
1 + -1m = 0

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

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

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

Divide each side by '-1'.
m = 1

Simplifying
m = 1
Solution
m = {-0.5, 1}