-4m^2+12m-6=0

Solution for -4m^2+12m-6=0 equation:

Simplifying
-4m2 + 12m + -6 = 0

Reorder the terms:
-6 + 12m + -4m2 = 0

Solving
-6 + 12m + -4m2 = 0

Solving for variable 'm'.

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

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

Simplifying
-3 + 6m + -2m2 = 0

Solving
-3 + 6m + -2m2 = 0

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

Divide each side by '-2'.
1.5 + -3m + m2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -3m + -1.5 + m2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -3m + m2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -3m + m2 = 0 + -1.5
-3m + m2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-3m + m2 = -1.5

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 = -1.5 + 2.25

Reorder the terms:
2.25 + -3m + m2 = -1.5 + 2.25

Combine like terms: -1.5 + 2.25 = 0.75
2.25 + -3m + m2 = 0.75

Factor a perfect square on the left side:
(m + -1.5)(m + -1.5) = 0.75

Calculate the square root of the right side: 0.866025404

Break this problem into two subproblems by setting 
(m + -1.5) equal to 0.866025404 and -0.866025404.

Subproblem 1
m + -1.5 = 0.866025404

Simplifying
m + -1.5 = 0.866025404

Reorder the terms:
-1.5 + m = 0.866025404

Solving
-1.5 + m = 0.866025404

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 = 0.866025404 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + m = 0.866025404 + 1.5
m = 0.866025404 + 1.5

Combine like terms: 0.866025404 + 1.5 = 2.366025404
m = 2.366025404

Simplifying
m = 2.366025404

Subproblem 2
m + -1.5 = -0.866025404

Simplifying
m + -1.5 = -0.866025404

Reorder the terms:
-1.5 + m = -0.866025404

Solving
-1.5 + m = -0.866025404

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 = -0.866025404 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + m = -0.866025404 + 1.5
m = -0.866025404 + 1.5

Combine like terms: -0.866025404 + 1.5 = 0.633974596
m = 0.633974596

Simplifying
m = 0.633974596

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {2.366025404, 0.633974596}
Solution
m = {2.366025404, 0.633974596}