6m^2-12m-88=-6

Solution for 6m^2-12m-88=-6 equation:

Simplifying
6m2 + -12m + -88 = -6

Reorder the terms:
-88 + -12m + 6m2 = -6

Solving
-88 + -12m + 6m2 = -6

Solving for variable 'm'.

Reorder the terms:
-88 + 6 + -12m + 6m2 = -6 + 6

Combine like terms: -88 + 6 = -82
-82 + -12m + 6m2 = -6 + 6

Combine like terms: -6 + 6 = 0
-82 + -12m + 6m2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-41 + -6m + 3m2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-41 + -6m + 3m2)' equal to zero and attempt to solve:

Simplifying
-41 + -6m + 3m2 = 0

Solving
-41 + -6m + 3m2 = 0

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

Divide each side by '3'.
-13.66666667 + -2m + m2 = 0

Move the constant term to the right:

Add '13.66666667' to each side of the equation.
-13.66666667 + -2m + 13.66666667 + m2 = 0 + 13.66666667

Reorder the terms:
-13.66666667 + 13.66666667 + -2m + m2 = 0 + 13.66666667

Combine like terms: -13.66666667 + 13.66666667 = 0.00000000
0.00000000 + -2m + m2 = 0 + 13.66666667
-2m + m2 = 0 + 13.66666667

Combine like terms: 0 + 13.66666667 = 13.66666667
-2m + m2 = 13.66666667

The m term is -2m.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2m + 1 + m2 = 13.66666667 + 1

Reorder the terms:
1 + -2m + m2 = 13.66666667 + 1

Combine like terms: 13.66666667 + 1 = 14.66666667
1 + -2m + m2 = 14.66666667

Factor a perfect square on the left side:
(m + -1)(m + -1) = 14.66666667

Calculate the square root of the right side: 3.829708431

Break this problem into two subproblems by setting 
(m + -1) equal to 3.829708431 and -3.829708431.

Subproblem 1
m + -1 = 3.829708431

Simplifying
m + -1 = 3.829708431

Reorder the terms:
-1 + m = 3.829708431

Solving
-1 + m = 3.829708431

Solving for variable 'm'.

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

Add '1' to each side of the equation.
-1 + 1 + m = 3.829708431 + 1

Combine like terms: -1 + 1 = 0
0 + m = 3.829708431 + 1
m = 3.829708431 + 1

Combine like terms: 3.829708431 + 1 = 4.829708431
m = 4.829708431

Simplifying
m = 4.829708431

Subproblem 2
m + -1 = -3.829708431

Simplifying
m + -1 = -3.829708431

Reorder the terms:
-1 + m = -3.829708431

Solving
-1 + m = -3.829708431

Solving for variable 'm'.

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

Add '1' to each side of the equation.
-1 + 1 + m = -3.829708431 + 1

Combine like terms: -1 + 1 = 0
0 + m = -3.829708431 + 1
m = -3.829708431 + 1

Combine like terms: -3.829708431 + 1 = -2.829708431
m = -2.829708431

Simplifying
m = -2.829708431

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {4.829708431, -2.829708431}
Solution
m = {4.829708431, -2.829708431}