6k^2-12k-90=8

Solution for 6k^2-12k-90=8 equation:

Simplifying
6k2 + -12k + -90 = 8

Reorder the terms:
-90 + -12k + 6k2 = 8

Solving
-90 + -12k + 6k2 = 8

Solving for variable 'k'.

Reorder the terms:
-90 + -8 + -12k + 6k2 = 8 + -8

Combine like terms: -90 + -8 = -98
-98 + -12k + 6k2 = 8 + -8

Combine like terms: 8 + -8 = 0
-98 + -12k + 6k2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-49 + -6k + 3k2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-49 + -6k + 3k2)' equal to zero and attempt to solve:

Simplifying
-49 + -6k + 3k2 = 0

Solving
-49 + -6k + 3k2 = 0

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

Divide each side by '3'.
-16.33333333 + -2k + k2 = 0

Move the constant term to the right:

Add '16.33333333' to each side of the equation.
-16.33333333 + -2k + 16.33333333 + k2 = 0 + 16.33333333

Reorder the terms:
-16.33333333 + 16.33333333 + -2k + k2 = 0 + 16.33333333

Combine like terms: -16.33333333 + 16.33333333 = 0.00000000
0.00000000 + -2k + k2 = 0 + 16.33333333
-2k + k2 = 0 + 16.33333333

Combine like terms: 0 + 16.33333333 = 16.33333333
-2k + k2 = 16.33333333

The k term is -2k.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2k + 1 + k2 = 16.33333333 + 1

Reorder the terms:
1 + -2k + k2 = 16.33333333 + 1

Combine like terms: 16.33333333 + 1 = 17.33333333
1 + -2k + k2 = 17.33333333

Factor a perfect square on the left side:
(k + -1)(k + -1) = 17.33333333

Calculate the square root of the right side: 4.163331999

Break this problem into two subproblems by setting 
(k + -1) equal to 4.163331999 and -4.163331999.

Subproblem 1
k + -1 = 4.163331999

Simplifying
k + -1 = 4.163331999

Reorder the terms:
-1 + k = 4.163331999

Solving
-1 + k = 4.163331999

Solving for variable 'k'.

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

Add '1' to each side of the equation.
-1 + 1 + k = 4.163331999 + 1

Combine like terms: -1 + 1 = 0
0 + k = 4.163331999 + 1
k = 4.163331999 + 1

Combine like terms: 4.163331999 + 1 = 5.163331999
k = 5.163331999

Simplifying
k = 5.163331999

Subproblem 2
k + -1 = -4.163331999

Simplifying
k + -1 = -4.163331999

Reorder the terms:
-1 + k = -4.163331999

Solving
-1 + k = -4.163331999

Solving for variable 'k'.

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

Add '1' to each side of the equation.
-1 + 1 + k = -4.163331999 + 1

Combine like terms: -1 + 1 = 0
0 + k = -4.163331999 + 1
k = -4.163331999 + 1

Combine like terms: -4.163331999 + 1 = -3.163331999
k = -3.163331999

Simplifying
k = -3.163331999

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {5.163331999, -3.163331999}
Solution
k = {5.163331999, -3.163331999}