6k^2=-8k+6

Solution for 6k^2=-8k+6 equation:

Simplifying
6k2 = -8k + 6

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

Solving
6k2 = 6 + -8k

Solving for variable 'k'.

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

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

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

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

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 4k + 3k2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + 4k + 3k2)' equal to zero and attempt to solve:

Simplifying
-3 + 4k + 3k2 = 0

Solving
-3 + 4k + 3k2 = 0

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

Divide each side by '3'.
-1 + 1.333333333k + k2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 1.333333333k + 1 + k2 = 0 + 1

Reorder the terms:
-1 + 1 + 1.333333333k + k2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 1.333333333k + k2 = 0 + 1
1.333333333k + k2 = 0 + 1

Combine like terms: 0 + 1 = 1
1.333333333k + k2 = 1

The k term is 1.333333333k.  Take half its coefficient (0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
1.333333333k + 0.4444444442 + k2 = 1 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333k + k2 = 1 + 0.4444444442

Combine like terms: 1 + 0.4444444442 = 1.4444444442
0.4444444442 + 1.333333333k + k2 = 1.4444444442

Factor a perfect square on the left side:
(k + 0.6666666665)(k + 0.6666666665) = 1.4444444442

Calculate the square root of the right side: 1.201850425

Break this problem into two subproblems by setting 
(k + 0.6666666665) equal to 1.201850425 and -1.201850425.

Subproblem 1
k + 0.6666666665 = 1.201850425

Simplifying
k + 0.6666666665 = 1.201850425

Reorder the terms:
0.6666666665 + k = 1.201850425

Solving
0.6666666665 + k = 1.201850425

Solving for variable 'k'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + k = 1.201850425 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + k = 1.201850425 + -0.6666666665
k = 1.201850425 + -0.6666666665

Combine like terms: 1.201850425 + -0.6666666665 = 0.5351837585
k = 0.5351837585

Simplifying
k = 0.5351837585

Subproblem 2
k + 0.6666666665 = -1.201850425

Simplifying
k + 0.6666666665 = -1.201850425

Reorder the terms:
0.6666666665 + k = -1.201850425

Solving
0.6666666665 + k = -1.201850425

Solving for variable 'k'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + k = -1.201850425 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + k = -1.201850425 + -0.6666666665
k = -1.201850425 + -0.6666666665

Combine like terms: -1.201850425 + -0.6666666665 = -1.8685170915
k = -1.8685170915

Simplifying
k = -1.8685170915

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.5351837585, -1.8685170915}
Solution
k = {0.5351837585, -1.8685170915}