2(m-5)(m-6)=112

Solution for 2(m-5)(m-6)=112 equation:

Simplifying
2(m + -5)(m + -6) = 112

Reorder the terms:
2(-5 + m)(m + -6) = 112

Reorder the terms:
2(-5 + m)(-6 + m) = 112

Multiply (-5 + m) * (-6 + m)
2(-5(-6 + m) + m(-6 + m)) = 112
2((-6 * -5 + m * -5) + m(-6 + m)) = 112
2((30 + -5m) + m(-6 + m)) = 112
2(30 + -5m + (-6 * m + m * m)) = 112
2(30 + -5m + (-6m + m2)) = 112

Combine like terms: -5m + -6m = -11m
2(30 + -11m + m2) = 112
(30 * 2 + -11m * 2 + m2 * 2) = 112
(60 + -22m + 2m2) = 112

Solving
60 + -22m + 2m2 = 112

Solving for variable 'm'.

Reorder the terms:
60 + -112 + -22m + 2m2 = 112 + -112

Combine like terms: 60 + -112 = -52
-52 + -22m + 2m2 = 112 + -112

Combine like terms: 112 + -112 = 0
-52 + -22m + 2m2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-26 + -11m + m2) = 0

Factor a trinomial.
2((-2 + -1m)(13 + -1m)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(13 + -1m)' equal to zero and attempt to solve:

Simplifying
13 + -1m = 0

Solving
13 + -1m = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1m = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1m = 0 + -13
-1m = 0 + -13

Combine like terms: 0 + -13 = -13
-1m = -13

Divide each side by '-1'.
m = 13

Simplifying
m = 13
Solution
m = {-2, 13}