12k(2k+11)=12(2k+12)

Solution for 12k(2k+11)=12(2k+12) equation:

Simplifying
12k(2k + 11) = 12(2k + 12)

Reorder the terms:
12k(11 + 2k) = 12(2k + 12)
(11 * 12k + 2k * 12k) = 12(2k + 12)
(132k + 24k2) = 12(2k + 12)

Reorder the terms:
132k + 24k2 = 12(12 + 2k)
132k + 24k2 = (12 * 12 + 2k * 12)
132k + 24k2 = (144 + 24k)

Solving
132k + 24k2 = 144 + 24k

Solving for variable 'k'.

Reorder the terms:
-144 + 132k + -24k + 24k2 = 144 + 24k + -144 + -24k

Combine like terms: 132k + -24k = 108k
-144 + 108k + 24k2 = 144 + 24k + -144 + -24k

Reorder the terms:
-144 + 108k + 24k2 = 144 + -144 + 24k + -24k

Combine like terms: 144 + -144 = 0
-144 + 108k + 24k2 = 0 + 24k + -24k
-144 + 108k + 24k2 = 24k + -24k

Combine like terms: 24k + -24k = 0
-144 + 108k + 24k2 = 0

Factor out the Greatest Common Factor (GCF), '12'.
12(-12 + 9k + 2k2) = 0

Ignore the factor 12.
Subproblem 1
Set the factor '(-12 + 9k + 2k2)' equal to zero and attempt to solve:

Simplifying
-12 + 9k + 2k2 = 0

Solving
-12 + 9k + 2k2 = 0

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

Divide each side by '2'.
-6 + 4.5k + k2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 4.5k + 6 + k2 = 0 + 6

Reorder the terms:
-6 + 6 + 4.5k + k2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 4.5k + k2 = 0 + 6
4.5k + k2 = 0 + 6

Combine like terms: 0 + 6 = 6
4.5k + k2 = 6

The k term is 4.5k.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5k + 5.0625 + k2 = 6 + 5.0625

Reorder the terms:
5.0625 + 4.5k + k2 = 6 + 5.0625

Combine like terms: 6 + 5.0625 = 11.0625
5.0625 + 4.5k + k2 = 11.0625

Factor a perfect square on the left side:
(k + 2.25)(k + 2.25) = 11.0625

Calculate the square root of the right side: 3.326033674

Break this problem into two subproblems by setting 
(k + 2.25) equal to 3.326033674 and -3.326033674.

Subproblem 1
k + 2.25 = 3.326033674

Simplifying
k + 2.25 = 3.326033674

Reorder the terms:
2.25 + k = 3.326033674

Solving
2.25 + k = 3.326033674

Solving for variable 'k'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + k = 3.326033674 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + k = 3.326033674 + -2.25
k = 3.326033674 + -2.25

Combine like terms: 3.326033674 + -2.25 = 1.076033674
k = 1.076033674

Simplifying
k = 1.076033674

Subproblem 2
k + 2.25 = -3.326033674

Simplifying
k + 2.25 = -3.326033674

Reorder the terms:
2.25 + k = -3.326033674

Solving
2.25 + k = -3.326033674

Solving for variable 'k'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + k = -3.326033674 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + k = -3.326033674 + -2.25
k = -3.326033674 + -2.25

Combine like terms: -3.326033674 + -2.25 = -5.576033674
k = -5.576033674

Simplifying
k = -5.576033674

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {1.076033674, -5.576033674}
Solution
k = {1.076033674, -5.576033674}