6m^2+12m+3=0

Solution for 6m^2+12m+3=0 equation:

Simplifying
6m2 + 12m + 3 = 0

Reorder the terms:
3 + 12m + 6m2 = 0

Solving
3 + 12m + 6m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + 4m + 2m2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(1 + 4m + 2m2)' equal to zero and attempt to solve:

Simplifying
1 + 4m + 2m2 = 0

Solving
1 + 4m + 2m2 = 0

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

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

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 2m + -0.5 + m2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 2m + m2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 2m + m2 = 0 + -0.5
2m + m2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
2m + m2 = -0.5

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 = -0.5 + 1

Reorder the terms:
1 + 2m + m2 = -0.5 + 1

Combine like terms: -0.5 + 1 = 0.5
1 + 2m + m2 = 0.5

Factor a perfect square on the left side:
(m + 1)(m + 1) = 0.5

Calculate the square root of the right side: 0.707106781

Break this problem into two subproblems by setting 
(m + 1) equal to 0.707106781 and -0.707106781.

Subproblem 1
m + 1 = 0.707106781

Simplifying
m + 1 = 0.707106781

Reorder the terms:
1 + m = 0.707106781

Solving
1 + m = 0.707106781

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 = 0.707106781 + -1

Combine like terms: 1 + -1 = 0
0 + m = 0.707106781 + -1
m = 0.707106781 + -1

Combine like terms: 0.707106781 + -1 = -0.292893219
m = -0.292893219

Simplifying
m = -0.292893219

Subproblem 2
m + 1 = -0.707106781

Simplifying
m + 1 = -0.707106781

Reorder the terms:
1 + m = -0.707106781

Solving
1 + m = -0.707106781

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 = -0.707106781 + -1

Combine like terms: 1 + -1 = 0
0 + m = -0.707106781 + -1
m = -0.707106781 + -1

Combine like terms: -0.707106781 + -1 = -1.707106781
m = -1.707106781

Simplifying
m = -1.707106781

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-0.292893219, -1.707106781}
Solution
m = {-0.292893219, -1.707106781}