4k(k+6)=6

Solution for 4k(k+6)=6 equation:

Simplifying
4k(k + 6) = 6

Reorder the terms:
4k(6 + k) = 6
(6 * 4k + k * 4k) = 6
(24k + 4k2) = 6

Solving
24k + 4k2 = 6

Solving for variable 'k'.

Reorder the terms:
-6 + 24k + 4k2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + 24k + 4k2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 12k + 2k2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + 12k + 2k2)' equal to zero and attempt to solve:

Simplifying
-3 + 12k + 2k2 = 0

Solving
-3 + 12k + 2k2 = 0

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

Divide each side by '2'.
-1.5 + 6k + k2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 6k + 1.5 + k2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 6k + k2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 6k + k2 = 0 + 1.5
6k + k2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
6k + k2 = 1.5

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 = 1.5 + 9

Reorder the terms:
9 + 6k + k2 = 1.5 + 9

Combine like terms: 1.5 + 9 = 10.5
9 + 6k + k2 = 10.5

Factor a perfect square on the left side:
(k + 3)(k + 3) = 10.5

Calculate the square root of the right side: 3.240370349

Break this problem into two subproblems by setting 
(k + 3) equal to 3.240370349 and -3.240370349.

Subproblem 1
k + 3 = 3.240370349

Simplifying
k + 3 = 3.240370349

Reorder the terms:
3 + k = 3.240370349

Solving
3 + k = 3.240370349

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 = 3.240370349 + -3

Combine like terms: 3 + -3 = 0
0 + k = 3.240370349 + -3
k = 3.240370349 + -3

Combine like terms: 3.240370349 + -3 = 0.240370349
k = 0.240370349

Simplifying
k = 0.240370349

Subproblem 2
k + 3 = -3.240370349

Simplifying
k + 3 = -3.240370349

Reorder the terms:
3 + k = -3.240370349

Solving
3 + k = -3.240370349

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 = -3.240370349 + -3

Combine like terms: 3 + -3 = 0
0 + k = -3.240370349 + -3
k = -3.240370349 + -3

Combine like terms: -3.240370349 + -3 = -6.240370349
k = -6.240370349

Simplifying
k = -6.240370349

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.240370349, -6.240370349}
Solution
k = {0.240370349, -6.240370349}