4m^2-12m-2=0

Solution for 4m^2-12m-2=0 equation:

Simplifying
4m2 + -12m + -2 = 0

Reorder the terms:
-2 + -12m + 4m2 = 0

Solving
-2 + -12m + 4m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -6m + 2m2) = 0

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

Simplifying
-1 + -6m + 2m2 = 0

Solving
-1 + -6m + 2m2 = 0

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

Divide each side by '2'.
-0.5 + -3m + m2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -3m + 0.5 + m2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -3m + m2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -3m + m2 = 0 + 0.5
-3m + m2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-3m + m2 = 0.5

The m term is -3m.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3m + 2.25 + m2 = 0.5 + 2.25

Reorder the terms:
2.25 + -3m + m2 = 0.5 + 2.25

Combine like terms: 0.5 + 2.25 = 2.75
2.25 + -3m + m2 = 2.75

Factor a perfect square on the left side:
(m + -1.5)(m + -1.5) = 2.75

Calculate the square root of the right side: 1.658312395

Break this problem into two subproblems by setting 
(m + -1.5) equal to 1.658312395 and -1.658312395.

Subproblem 1
m + -1.5 = 1.658312395

Simplifying
m + -1.5 = 1.658312395

Reorder the terms:
-1.5 + m = 1.658312395

Solving
-1.5 + m = 1.658312395

Solving for variable 'm'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + m = 1.658312395 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + m = 1.658312395 + 1.5
m = 1.658312395 + 1.5

Combine like terms: 1.658312395 + 1.5 = 3.158312395
m = 3.158312395

Simplifying
m = 3.158312395

Subproblem 2
m + -1.5 = -1.658312395

Simplifying
m + -1.5 = -1.658312395

Reorder the terms:
-1.5 + m = -1.658312395

Solving
-1.5 + m = -1.658312395

Solving for variable 'm'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + m = -1.658312395 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + m = -1.658312395 + 1.5
m = -1.658312395 + 1.5

Combine like terms: -1.658312395 + 1.5 = -0.158312395
m = -0.158312395

Simplifying
m = -0.158312395

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {3.158312395, -0.158312395}
Solution
m = {3.158312395, -0.158312395}