6m(m-6)=4(6-m)

Solution for 6m(m-6)=4(6-m) equation:

Simplifying
6m(m + -6) = 4(6 + -1m)

Reorder the terms:
6m(-6 + m) = 4(6 + -1m)
(-6 * 6m + m * 6m) = 4(6 + -1m)
(-36m + 6m2) = 4(6 + -1m)
-36m + 6m2 = (6 * 4 + -1m * 4)
-36m + 6m2 = (24 + -4m)

Solving
-36m + 6m2 = 24 + -4m

Solving for variable 'm'.

Reorder the terms:
-24 + -36m + 4m + 6m2 = 24 + -4m + -24 + 4m

Combine like terms: -36m + 4m = -32m
-24 + -32m + 6m2 = 24 + -4m + -24 + 4m

Reorder the terms:
-24 + -32m + 6m2 = 24 + -24 + -4m + 4m

Combine like terms: 24 + -24 = 0
-24 + -32m + 6m2 = 0 + -4m + 4m
-24 + -32m + 6m2 = -4m + 4m

Combine like terms: -4m + 4m = 0
-24 + -32m + 6m2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + -16m + 3m2) = 0

Factor a trinomial.
2((-2 + -3m)(6 + -1m)) = 0

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

Simplifying
-2 + -3m = 0

Solving
-2 + -3m = 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 + -3m = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3m = 0 + 2
-3m = 0 + 2

Combine like terms: 0 + 2 = 2
-3m = 2

Divide each side by '-3'.
m = -0.6666666667

Simplifying
m = -0.6666666667
Subproblem 2
Set the factor '(6 + -1m)' equal to zero and attempt to solve:

Simplifying
6 + -1m = 0

Solving
6 + -1m = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1m = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1m = 0 + -6
-1m = 0 + -6

Combine like terms: 0 + -6 = -6
-1m = -6

Divide each side by '-1'.
m = 6

Simplifying
m = 6
Solution
m = {-0.6666666667, 6}