-(2m-6)(-9m+6)=m-10-7m+10

Solution for -(2m-6)(-9m+6)=m-10-7m+10 equation:

Simplifying
-1(2m + -6)(-9m + 6) = m + -10 + -7m + 10

Reorder the terms:
-1(-6 + 2m)(-9m + 6) = m + -10 + -7m + 10

Reorder the terms:
-1(-6 + 2m)(6 + -9m) = m + -10 + -7m + 10

Multiply (-6 + 2m) * (6 + -9m)
-1(-6(6 + -9m) + 2m * (6 + -9m)) = m + -10 + -7m + 10
-1((6 * -6 + -9m * -6) + 2m * (6 + -9m)) = m + -10 + -7m + 10
-1((-36 + 54m) + 2m * (6 + -9m)) = m + -10 + -7m + 10
-1(-36 + 54m + (6 * 2m + -9m * 2m)) = m + -10 + -7m + 10
-1(-36 + 54m + (12m + -18m2)) = m + -10 + -7m + 10

Combine like terms: 54m + 12m = 66m
-1(-36 + 66m + -18m2) = m + -10 + -7m + 10
(-36 * -1 + 66m * -1 + -18m2 * -1) = m + -10 + -7m + 10
(36 + -66m + 18m2) = m + -10 + -7m + 10

Reorder the terms:
36 + -66m + 18m2 = -10 + 10 + m + -7m

Combine like terms: -10 + 10 = 0
36 + -66m + 18m2 = 0 + m + -7m
36 + -66m + 18m2 = m + -7m

Combine like terms: m + -7m = -6m
36 + -66m + 18m2 = -6m

Solving
36 + -66m + 18m2 = -6m

Solving for variable 'm'.

Reorder the terms:
36 + -66m + 6m + 18m2 = -6m + 6m

Combine like terms: -66m + 6m = -60m
36 + -60m + 18m2 = -6m + 6m

Combine like terms: -6m + 6m = 0
36 + -60m + 18m2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(6 + -10m + 3m2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(6 + -10m + 3m2)' equal to zero and attempt to solve:

Simplifying
6 + -10m + 3m2 = 0

Solving
6 + -10m + 3m2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
2 + -3.333333333m + m2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -3.333333333m + -2 + m2 = 0 + -2

Reorder the terms:
2 + -2 + -3.333333333m + m2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3.333333333m + m2 = 0 + -2
-3.333333333m + m2 = 0 + -2

Combine like terms: 0 + -2 = -2
-3.333333333m + m2 = -2

The m term is -3.333333333m.  Take half its coefficient (-1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
-3.333333333m + 2.777777779 + m2 = -2 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333m + m2 = -2 + 2.777777779

Combine like terms: -2 + 2.777777779 = 0.777777779
2.777777779 + -3.333333333m + m2 = 0.777777779

Factor a perfect square on the left side:
(m + -1.666666667)(m + -1.666666667) = 0.777777779

Calculate the square root of the right side: 0.881917104

Break this problem into two subproblems by setting 
(m + -1.666666667) equal to 0.881917104 and -0.881917104.

Subproblem 1
m + -1.666666667 = 0.881917104

Simplifying
m + -1.666666667 = 0.881917104

Reorder the terms:
-1.666666667 + m = 0.881917104

Solving
-1.666666667 + m = 0.881917104

Solving for variable 'm'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + m = 0.881917104 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + m = 0.881917104 + 1.666666667
m = 0.881917104 + 1.666666667

Combine like terms: 0.881917104 + 1.666666667 = 2.548583771
m = 2.548583771

Simplifying
m = 2.548583771

Subproblem 2
m + -1.666666667 = -0.881917104

Simplifying
m + -1.666666667 = -0.881917104

Reorder the terms:
-1.666666667 + m = -0.881917104

Solving
-1.666666667 + m = -0.881917104

Solving for variable 'm'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + m = -0.881917104 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + m = -0.881917104 + 1.666666667
m = -0.881917104 + 1.666666667

Combine like terms: -0.881917104 + 1.666666667 = 0.784749563
m = 0.784749563

Simplifying
m = 0.784749563

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {2.548583771, 0.784749563}
Solution
m = {2.548583771, 0.784749563}