6m^2-12m-88=4

Solution for 6m^2-12m-88=4 equation:

Simplifying
6m2 + -12m + -88 = 4

Reorder the terms:
-88 + -12m + 6m2 = 4

Solving
-88 + -12m + 6m2 = 4

Solving for variable 'm'.

Reorder the terms:
-88 + -4 + -12m + 6m2 = 4 + -4

Combine like terms: -88 + -4 = -92
-92 + -12m + 6m2 = 4 + -4

Combine like terms: 4 + -4 = 0
-92 + -12m + 6m2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-46 + -6m + 3m2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-46 + -6m + 3m2)' equal to zero and attempt to solve:

Simplifying
-46 + -6m + 3m2 = 0

Solving
-46 + -6m + 3m2 = 0

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

Divide each side by '3'.
-15.33333333 + -2m + m2 = 0

Move the constant term to the right:

Add '15.33333333' to each side of the equation.
-15.33333333 + -2m + 15.33333333 + m2 = 0 + 15.33333333

Reorder the terms:
-15.33333333 + 15.33333333 + -2m + m2 = 0 + 15.33333333

Combine like terms: -15.33333333 + 15.33333333 = 0.00000000
0.00000000 + -2m + m2 = 0 + 15.33333333
-2m + m2 = 0 + 15.33333333

Combine like terms: 0 + 15.33333333 = 15.33333333
-2m + m2 = 15.33333333

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 = 15.33333333 + 1

Reorder the terms:
1 + -2m + m2 = 15.33333333 + 1

Combine like terms: 15.33333333 + 1 = 16.33333333
1 + -2m + m2 = 16.33333333

Factor a perfect square on the left side:
(m + -1)(m + -1) = 16.33333333

Calculate the square root of the right side: 4.041451884

Break this problem into two subproblems by setting 
(m + -1) equal to 4.041451884 and -4.041451884.

Subproblem 1
m + -1 = 4.041451884

Simplifying
m + -1 = 4.041451884

Reorder the terms:
-1 + m = 4.041451884

Solving
-1 + m = 4.041451884

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 = 4.041451884 + 1

Combine like terms: -1 + 1 = 0
0 + m = 4.041451884 + 1
m = 4.041451884 + 1

Combine like terms: 4.041451884 + 1 = 5.041451884
m = 5.041451884

Simplifying
m = 5.041451884

Subproblem 2
m + -1 = -4.041451884

Simplifying
m + -1 = -4.041451884

Reorder the terms:
-1 + m = -4.041451884

Solving
-1 + m = -4.041451884

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 = -4.041451884 + 1

Combine like terms: -1 + 1 = 0
0 + m = -4.041451884 + 1
m = -4.041451884 + 1

Combine like terms: -4.041451884 + 1 = -3.041451884
m = -3.041451884

Simplifying
m = -3.041451884

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {5.041451884, -3.041451884}
Solution
m = {5.041451884, -3.041451884}