6m^2+12m+1=0

Solution for 6m^2+12m+1=0 equation:

Simplifying
6m2 + 12m + 1 = 0

Reorder the terms:
1 + 12m + 6m2 = 0

Solving
1 + 12m + 6m2 = 0

Solving for variable 'm'.

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

Divide each side by '6'.
0.1666666667 + 2m + m2 = 0

Move the constant term to the right:

Add '-0.1666666667' to each side of the equation.
0.1666666667 + 2m + -0.1666666667 + m2 = 0 + -0.1666666667

Reorder the terms:
0.1666666667 + -0.1666666667 + 2m + m2 = 0 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + 2m + m2 = 0 + -0.1666666667
2m + m2 = 0 + -0.1666666667

Combine like terms: 0 + -0.1666666667 = -0.1666666667
2m + m2 = -0.1666666667

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 = -0.1666666667 + 1

Reorder the terms:
1 + 2m + m2 = -0.1666666667 + 1

Combine like terms: -0.1666666667 + 1 = 0.8333333333
1 + 2m + m2 = 0.8333333333

Factor a perfect square on the left side:
(m + 1)(m + 1) = 0.8333333333

Calculate the square root of the right side: 0.912870929

Break this problem into two subproblems by setting 
(m + 1) equal to 0.912870929 and -0.912870929.

Subproblem 1
m + 1 = 0.912870929

Simplifying
m + 1 = 0.912870929

Reorder the terms:
1 + m = 0.912870929

Solving
1 + m = 0.912870929

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 = 0.912870929 + -1

Combine like terms: 1 + -1 = 0
0 + m = 0.912870929 + -1
m = 0.912870929 + -1

Combine like terms: 0.912870929 + -1 = -0.087129071
m = -0.087129071

Simplifying
m = -0.087129071

Subproblem 2
m + 1 = -0.912870929

Simplifying
m + 1 = -0.912870929

Reorder the terms:
1 + m = -0.912870929

Solving
1 + m = -0.912870929

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 = -0.912870929 + -1

Combine like terms: 1 + -1 = 0
0 + m = -0.912870929 + -1
m = -0.912870929 + -1

Combine like terms: -0.912870929 + -1 = -1.912870929
m = -1.912870929

Simplifying
m = -1.912870929

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-0.087129071, -1.912870929}