0=2k(k+6)+6

Solution for 0=2k(k+6)+6 equation:

Simplifying
0 = 2k(k + 6) + 6

Reorder the terms:
0 = 2k(6 + k) + 6
0 = (6 * 2k + k * 2k) + 6
0 = (12k + 2k2) + 6

Reorder the terms:
0 = 6 + 12k + 2k2

Solving
0 = 6 + 12k + 2k2

Solving for variable 'k'.

Combine like terms: 0 + -6 = -6
-6 + -12k + -2k2 = 6 + 12k + 2k2 + -6 + -12k + -2k2

Reorder the terms:
-6 + -12k + -2k2 = 6 + -6 + 12k + -12k + 2k2 + -2k2

Combine like terms: 6 + -6 = 0
-6 + -12k + -2k2 = 0 + 12k + -12k + 2k2 + -2k2
-6 + -12k + -2k2 = 12k + -12k + 2k2 + -2k2

Combine like terms: 12k + -12k = 0
-6 + -12k + -2k2 = 0 + 2k2 + -2k2
-6 + -12k + -2k2 = 2k2 + -2k2

Combine like terms: 2k2 + -2k2 = 0
-6 + -12k + -2k2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(3 + 6k + k2) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(3 + 6k + k2)' equal to zero and attempt to solve:

Simplifying
3 + 6k + k2 = 0

Solving
3 + 6k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 6k + -3 + k2 = 0 + -3

Reorder the terms:
3 + -3 + 6k + k2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 6k + k2 = 0 + -3
6k + k2 = 0 + -3

Combine like terms: 0 + -3 = -3
6k + k2 = -3

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

Add '9' to each side of the equation.
6k + 9 + k2 = -3 + 9

Reorder the terms:
9 + 6k + k2 = -3 + 9

Combine like terms: -3 + 9 = 6
9 + 6k + k2 = 6

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

Calculate the square root of the right side: 2.449489743

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

Subproblem 1
k + 3 = 2.449489743

Simplifying
k + 3 = 2.449489743

Reorder the terms:
3 + k = 2.449489743

Solving
3 + k = 2.449489743

Solving for variable 'k'.

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

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

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

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

Simplifying
k = -0.550510257

Subproblem 2
k + 3 = -2.449489743

Simplifying
k + 3 = -2.449489743

Reorder the terms:
3 + k = -2.449489743

Solving
3 + k = -2.449489743

Solving for variable 'k'.

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

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

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

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

Simplifying
k = -5.449489743

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