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 = -0.633974596
m = -0.633974596

Simplifying
m = -0.633974596

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 = -2.366025404
m = -2.366025404

Simplifying
m = -2.366025404

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