4(k+2)-8k-5=3k+9-2k(k+6)

Solution for 4(k+2)-8k-5=3k+9-2k(k+6) equation:

Simplifying
4(k + 2) + -8k + -5 = 3k + 9 + -2k(k + 6)

Reorder the terms:
4(2 + k) + -8k + -5 = 3k + 9 + -2k(k + 6)
(2 * 4 + k * 4) + -8k + -5 = 3k + 9 + -2k(k + 6)
(8 + 4k) + -8k + -5 = 3k + 9 + -2k(k + 6)

Reorder the terms:
8 + -5 + 4k + -8k = 3k + 9 + -2k(k + 6)

Combine like terms: 8 + -5 = 3
3 + 4k + -8k = 3k + 9 + -2k(k + 6)

Combine like terms: 4k + -8k = -4k
3 + -4k = 3k + 9 + -2k(k + 6)

Reorder the terms:
3 + -4k = 3k + 9 + -2k(6 + k)
3 + -4k = 3k + 9 + (6 * -2k + k * -2k)
3 + -4k = 3k + 9 + (-12k + -2k2)

Reorder the terms:
3 + -4k = 9 + 3k + -12k + -2k2

Combine like terms: 3k + -12k = -9k
3 + -4k = 9 + -9k + -2k2

Solving
3 + -4k = 9 + -9k + -2k2

Solving for variable 'k'.

Reorder the terms:
3 + -9 + -4k + 9k + 2k2 = 9 + -9k + -2k2 + -9 + 9k + 2k2

Combine like terms: 3 + -9 = -6
-6 + -4k + 9k + 2k2 = 9 + -9k + -2k2 + -9 + 9k + 2k2

Combine like terms: -4k + 9k = 5k
-6 + 5k + 2k2 = 9 + -9k + -2k2 + -9 + 9k + 2k2

Reorder the terms:
-6 + 5k + 2k2 = 9 + -9 + -9k + 9k + -2k2 + 2k2

Combine like terms: 9 + -9 = 0
-6 + 5k + 2k2 = 0 + -9k + 9k + -2k2 + 2k2
-6 + 5k + 2k2 = -9k + 9k + -2k2 + 2k2

Combine like terms: -9k + 9k = 0
-6 + 5k + 2k2 = 0 + -2k2 + 2k2
-6 + 5k + 2k2 = -2k2 + 2k2

Combine like terms: -2k2 + 2k2 = 0
-6 + 5k + 2k2 = 0

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

Divide each side by '2'.
-3 + 2.5k + k2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 2.5k + 3 + k2 = 0 + 3

Reorder the terms:
-3 + 3 + 2.5k + k2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 2.5k + k2 = 0 + 3
2.5k + k2 = 0 + 3

Combine like terms: 0 + 3 = 3
2.5k + k2 = 3

The k term is 2.5k.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5k + 1.5625 + k2 = 3 + 1.5625

Reorder the terms:
1.5625 + 2.5k + k2 = 3 + 1.5625

Combine like terms: 3 + 1.5625 = 4.5625
1.5625 + 2.5k + k2 = 4.5625

Factor a perfect square on the left side:
(k + 1.25)(k + 1.25) = 4.5625

Calculate the square root of the right side: 2.136000936

Break this problem into two subproblems by setting 
(k + 1.25) equal to 2.136000936 and -2.136000936.

Subproblem 1
k + 1.25 = 2.136000936

Simplifying
k + 1.25 = 2.136000936

Reorder the terms:
1.25 + k = 2.136000936

Solving
1.25 + k = 2.136000936

Solving for variable 'k'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + k = 2.136000936 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + k = 2.136000936 + -1.25
k = 2.136000936 + -1.25

Combine like terms: 2.136000936 + -1.25 = 0.886000936
k = 0.886000936

Simplifying
k = 0.886000936

Subproblem 2
k + 1.25 = -2.136000936

Simplifying
k + 1.25 = -2.136000936

Reorder the terms:
1.25 + k = -2.136000936

Solving
1.25 + k = -2.136000936

Solving for variable 'k'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + k = -2.136000936 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + k = -2.136000936 + -1.25
k = -2.136000936 + -1.25

Combine like terms: -2.136000936 + -1.25 = -3.386000936
k = -3.386000936

Simplifying
k = -3.386000936

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.886000936, -3.386000936}