2m(m-7)-5(6m-6)=

Solution for 2m(m-7)-5(6m-6)= equation:

Simplifying
2m(m + -7) + -5(6m + -6) = 0

Reorder the terms:
2m(-7 + m) + -5(6m + -6) = 0
(-7 * 2m + m * 2m) + -5(6m + -6) = 0
(-14m + 2m2) + -5(6m + -6) = 0

Reorder the terms:
-14m + 2m2 + -5(-6 + 6m) = 0
-14m + 2m2 + (-6 * -5 + 6m * -5) = 0
-14m + 2m2 + (30 + -30m) = 0

Reorder the terms:
30 + -14m + -30m + 2m2 = 0

Combine like terms: -14m + -30m = -44m
30 + -44m + 2m2 = 0

Solving
30 + -44m + 2m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + -22m + m2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(15 + -22m + m2)' equal to zero and attempt to solve:

Simplifying
15 + -22m + m2 = 0

Solving
15 + -22m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + -22m + -15 + m2 = 0 + -15

Reorder the terms:
15 + -15 + -22m + m2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -22m + m2 = 0 + -15
-22m + m2 = 0 + -15

Combine like terms: 0 + -15 = -15
-22m + m2 = -15

The m term is -22m.  Take half its coefficient (-11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
-22m + 121 + m2 = -15 + 121

Reorder the terms:
121 + -22m + m2 = -15 + 121

Combine like terms: -15 + 121 = 106
121 + -22m + m2 = 106

Factor a perfect square on the left side:
(m + -11)(m + -11) = 106

Calculate the square root of the right side: 10.295630141

Break this problem into two subproblems by setting 
(m + -11) equal to 10.295630141 and -10.295630141.

Subproblem 1
m + -11 = 10.295630141

Simplifying
m + -11 = 10.295630141

Reorder the terms:
-11 + m = 10.295630141

Solving
-11 + m = 10.295630141

Solving for variable 'm'.

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

Add '11' to each side of the equation.
-11 + 11 + m = 10.295630141 + 11

Combine like terms: -11 + 11 = 0
0 + m = 10.295630141 + 11
m = 10.295630141 + 11

Combine like terms: 10.295630141 + 11 = 21.295630141
m = 21.295630141

Simplifying
m = 21.295630141

Subproblem 2
m + -11 = -10.295630141

Simplifying
m + -11 = -10.295630141

Reorder the terms:
-11 + m = -10.295630141

Solving
-11 + m = -10.295630141

Solving for variable 'm'.

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

Add '11' to each side of the equation.
-11 + 11 + m = -10.295630141 + 11

Combine like terms: -11 + 11 = 0
0 + m = -10.295630141 + 11
m = -10.295630141 + 11

Combine like terms: -10.295630141 + 11 = 0.704369859
m = 0.704369859

Simplifying
m = 0.704369859

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {21.295630141, 0.704369859}
Solution
m = {21.295630141, 0.704369859}