-6+5(8-k)8k=

Solution for -6+5(8-k)8k= equation:

Simplifying
-6 + 5(8 + -1k) * 8k = 0

Reorder the terms for easier multiplication:
-6 + 5 * 8k(8 + -1k) = 0

Multiply 5 * 8
-6 + 40k(8 + -1k) = 0
-6 + (8 * 40k + -1k * 40k) = 0
-6 + (320k + -40k2) = 0

Solving
-6 + 320k + -40k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 160k + -20k2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + 160k + -20k2)' equal to zero and attempt to solve:

Simplifying
-3 + 160k + -20k2 = 0

Solving
-3 + 160k + -20k2 = 0

Begin completing the square.  Divide all terms by
-20 the coefficient of the squared term: 

Divide each side by '-20'.
0.15 + -8k + k2 = 0.0

Move the constant term to the right:

Add '-0.15' to each side of the equation.
0.15 + -8k + -0.15 + k2 = 0.0 + -0.15

Reorder the terms:
0.15 + -0.15 + -8k + k2 = 0.0 + -0.15

Combine like terms: 0.15 + -0.15 = 0.00
0.00 + -8k + k2 = 0.0 + -0.15
-8k + k2 = 0.0 + -0.15

Combine like terms: 0.0 + -0.15 = -0.15
-8k + k2 = -0.15

The k term is -8k.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8k + 16 + k2 = -0.15 + 16

Reorder the terms:
16 + -8k + k2 = -0.15 + 16

Combine like terms: -0.15 + 16 = 15.85
16 + -8k + k2 = 15.85

Factor a perfect square on the left side:
(k + -4)(k + -4) = 15.85

Calculate the square root of the right side: 3.981205847

Break this problem into two subproblems by setting 
(k + -4) equal to 3.981205847 and -3.981205847.

Subproblem 1
k + -4 = 3.981205847

Simplifying
k + -4 = 3.981205847

Reorder the terms:
-4 + k = 3.981205847

Solving
-4 + k = 3.981205847

Solving for variable 'k'.

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

Add '4' to each side of the equation.
-4 + 4 + k = 3.981205847 + 4

Combine like terms: -4 + 4 = 0
0 + k = 3.981205847 + 4
k = 3.981205847 + 4

Combine like terms: 3.981205847 + 4 = 7.981205847
k = 7.981205847

Simplifying
k = 7.981205847

Subproblem 2
k + -4 = -3.981205847

Simplifying
k + -4 = -3.981205847

Reorder the terms:
-4 + k = -3.981205847

Solving
-4 + k = -3.981205847

Solving for variable 'k'.

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

Add '4' to each side of the equation.
-4 + 4 + k = -3.981205847 + 4

Combine like terms: -4 + 4 = 0
0 + k = -3.981205847 + 4
k = -3.981205847 + 4

Combine like terms: -3.981205847 + 4 = 0.018794153
k = 0.018794153

Simplifying
k = 0.018794153

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {7.981205847, 0.018794153}
Solution
k = {7.981205847, 0.018794153}