7m(m-6)=2(6-m)

Solution for 7m(m-6)=2(6-m) equation:

Simplifying
7m(m + -6) = 2(6 + -1m)

Reorder the terms:
7m(-6 + m) = 2(6 + -1m)
(-6 * 7m + m * 7m) = 2(6 + -1m)
(-42m + 7m2) = 2(6 + -1m)
-42m + 7m2 = (6 * 2 + -1m * 2)
-42m + 7m2 = (12 + -2m)

Solving
-42m + 7m2 = 12 + -2m

Solving for variable 'm'.

Reorder the terms:
-12 + -42m + 2m + 7m2 = 12 + -2m + -12 + 2m

Combine like terms: -42m + 2m = -40m
-12 + -40m + 7m2 = 12 + -2m + -12 + 2m

Reorder the terms:
-12 + -40m + 7m2 = 12 + -12 + -2m + 2m

Combine like terms: 12 + -12 = 0
-12 + -40m + 7m2 = 0 + -2m + 2m
-12 + -40m + 7m2 = -2m + 2m

Combine like terms: -2m + 2m = 0
-12 + -40m + 7m2 = 0

Factor a trinomial.
(-2 + -7m)(6 + -1m) = 0

Subproblem 1
Set the factor '(-2 + -7m)' equal to zero and attempt to solve:

Simplifying
-2 + -7m = 0

Solving
-2 + -7m = 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 + -7m = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -7m = 0 + 2
-7m = 0 + 2

Combine like terms: 0 + 2 = 2
-7m = 2

Divide each side by '-7'.
m = -0.2857142857

Simplifying
m = -0.2857142857
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 = {-0.2857142857, 6}