2(3k^2)-1=6(2k-1)

Solution for 2(3k^2)-1=6(2k-1) equation:

Simplifying
2(3k2) + -1 = 6(2k + -1)

Remove parenthesis around (3k2)
2 * 3k2 + -1 = 6(2k + -1)

Multiply 2 * 3
6k2 + -1 = 6(2k + -1)

Reorder the terms:
-1 + 6k2 = 6(2k + -1)

Reorder the terms:
-1 + 6k2 = 6(-1 + 2k)
-1 + 6k2 = (-1 * 6 + 2k * 6)
-1 + 6k2 = (-6 + 12k)

Solving
-1 + 6k2 = -6 + 12k

Solving for variable 'k'.

Reorder the terms:
-1 + 6 + -12k + 6k2 = -6 + 12k + 6 + -12k

Combine like terms: -1 + 6 = 5
5 + -12k + 6k2 = -6 + 12k + 6 + -12k

Reorder the terms:
5 + -12k + 6k2 = -6 + 6 + 12k + -12k

Combine like terms: -6 + 6 = 0
5 + -12k + 6k2 = 0 + 12k + -12k
5 + -12k + 6k2 = 12k + -12k

Combine like terms: 12k + -12k = 0
5 + -12k + 6k2 = 0

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

Divide each side by '6'.
0.8333333333 + -2k + k2 = 0

Move the constant term to the right:

Add '-0.8333333333' to each side of the equation.
0.8333333333 + -2k + -0.8333333333 + k2 = 0 + -0.8333333333

Reorder the terms:
0.8333333333 + -0.8333333333 + -2k + k2 = 0 + -0.8333333333

Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000
0.0000000000 + -2k + k2 = 0 + -0.8333333333
-2k + k2 = 0 + -0.8333333333

Combine like terms: 0 + -0.8333333333 = -0.8333333333
-2k + k2 = -0.8333333333

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 = -0.8333333333 + 1

Reorder the terms:
1 + -2k + k2 = -0.8333333333 + 1

Combine like terms: -0.8333333333 + 1 = 0.1666666667
1 + -2k + k2 = 0.1666666667

Factor a perfect square on the left side:
(k + -1)(k + -1) = 0.1666666667

Calculate the square root of the right side: 0.408248291

Break this problem into two subproblems by setting 
(k + -1) equal to 0.408248291 and -0.408248291.

Subproblem 1
k + -1 = 0.408248291

Simplifying
k + -1 = 0.408248291

Reorder the terms:
-1 + k = 0.408248291

Solving
-1 + k = 0.408248291

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 = 0.408248291 + 1

Combine like terms: -1 + 1 = 0
0 + k = 0.408248291 + 1
k = 0.408248291 + 1

Combine like terms: 0.408248291 + 1 = 1.408248291
k = 1.408248291

Simplifying
k = 1.408248291

Subproblem 2
k + -1 = -0.408248291

Simplifying
k + -1 = -0.408248291

Reorder the terms:
-1 + k = -0.408248291

Solving
-1 + k = -0.408248291

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 = -0.408248291 + 1

Combine like terms: -1 + 1 = 0
0 + k = -0.408248291 + 1
k = -0.408248291 + 1

Combine like terms: -0.408248291 + 1 = 0.591751709
k = 0.591751709

Simplifying
k = 0.591751709

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {1.408248291, 0.591751709}