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

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

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

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

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

Solving
132 + 24k = 144k + 24k2

Solving for variable 'k'.

Combine like terms: 24k + -144k = -120k
132 + -120k + -24k2 = 144k + 24k2 + -144k + -24k2

Reorder the terms:
132 + -120k + -24k2 = 144k + -144k + 24k2 + -24k2

Combine like terms: 144k + -144k = 0
132 + -120k + -24k2 = 0 + 24k2 + -24k2
132 + -120k + -24k2 = 24k2 + -24k2

Combine like terms: 24k2 + -24k2 = 0
132 + -120k + -24k2 = 0

Factor out the Greatest Common Factor (GCF), '12'.
12(11 + -10k + -2k2) = 0

Ignore the factor 12.
Subproblem 1
Set the factor '(11 + -10k + -2k2)' equal to zero and attempt to solve:

Simplifying
11 + -10k + -2k2 = 0

Solving
11 + -10k + -2k2 = 0

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

Divide each side by '-2'.
-5.5 + 5k + k2 = 0

Move the constant term to the right:

Add '5.5' to each side of the equation.
-5.5 + 5k + 5.5 + k2 = 0 + 5.5

Reorder the terms:
-5.5 + 5.5 + 5k + k2 = 0 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + 5k + k2 = 0 + 5.5
5k + k2 = 0 + 5.5

Combine like terms: 0 + 5.5 = 5.5
5k + k2 = 5.5

The k term is 5k.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5k + 6.25 + k2 = 5.5 + 6.25

Reorder the terms:
6.25 + 5k + k2 = 5.5 + 6.25

Combine like terms: 5.5 + 6.25 = 11.75
6.25 + 5k + k2 = 11.75

Factor a perfect square on the left side:
(k + 2.5)(k + 2.5) = 11.75

Calculate the square root of the right side: 3.4278273

Break this problem into two subproblems by setting 
(k + 2.5) equal to 3.4278273 and -3.4278273.

Subproblem 1
k + 2.5 = 3.4278273

Simplifying
k + 2.5 = 3.4278273

Reorder the terms:
2.5 + k = 3.4278273

Solving
2.5 + k = 3.4278273

Solving for variable 'k'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + k = 3.4278273 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + k = 3.4278273 + -2.5
k = 3.4278273 + -2.5

Combine like terms: 3.4278273 + -2.5 = 0.9278273
k = 0.9278273

Simplifying
k = 0.9278273

Subproblem 2
k + 2.5 = -3.4278273

Simplifying
k + 2.5 = -3.4278273

Reorder the terms:
2.5 + k = -3.4278273

Solving
2.5 + k = -3.4278273

Solving for variable 'k'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + k = -3.4278273 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + k = -3.4278273 + -2.5
k = -3.4278273 + -2.5

Combine like terms: -3.4278273 + -2.5 = -5.9278273
k = -5.9278273

Simplifying
k = -5.9278273

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.9278273, -5.9278273}
Solution
k = {0.9278273, -5.9278273}