2m(m+6)=-6

Solution for 2m(m+6)=-6 equation:

Simplifying
2m(m + 6) = -6

Reorder the terms:
2m(6 + m) = -6
(6 * 2m + m * 2m) = -6
(12m + 2m2) = -6

Solving
12m + 2m2 = -6

Solving for variable 'm'.

Reorder the terms:
6 + 12m + 2m2 = -6 + 6

Combine like terms: -6 + 6 = 0
6 + 12m + 2m2 = 0

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

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

Simplifying
3 + 6m + m2 = 0

Solving
3 + 6m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 6m + -3 + m2 = 0 + -3

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

Combine like terms: 3 + -3 = 0
0 + 6m + m2 = 0 + -3
6m + m2 = 0 + -3

Combine like terms: 0 + -3 = -3
6m + m2 = -3

The m term is 6m.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6m + 9 + m2 = -3 + 9

Reorder the terms:
9 + 6m + m2 = -3 + 9

Combine like terms: -3 + 9 = 6
9 + 6m + m2 = 6

Factor a perfect square on the left side:
(m + 3)(m + 3) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(m + 3) equal to 2.449489743 and -2.449489743.

Subproblem 1
m + 3 = 2.449489743

Simplifying
m + 3 = 2.449489743

Reorder the terms:
3 + m = 2.449489743

Solving
3 + m = 2.449489743

Solving for variable 'm'.

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

Add '-3' to each side of the equation.
3 + -3 + m = 2.449489743 + -3

Combine like terms: 3 + -3 = 0
0 + m = 2.449489743 + -3
m = 2.449489743 + -3

Combine like terms: 2.449489743 + -3 = -0.550510257
m = -0.550510257

Simplifying
m = -0.550510257

Subproblem 2
m + 3 = -2.449489743

Simplifying
m + 3 = -2.449489743

Reorder the terms:
3 + m = -2.449489743

Solving
3 + m = -2.449489743

Solving for variable 'm'.

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

Add '-3' to each side of the equation.
3 + -3 + m = -2.449489743 + -3

Combine like terms: 3 + -3 = 0
0 + m = -2.449489743 + -3
m = -2.449489743 + -3

Combine like terms: -2.449489743 + -3 = -5.449489743
m = -5.449489743

Simplifying
m = -5.449489743

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-0.550510257, -5.449489743}
Solution
m = {-0.550510257, -5.449489743}