-12k^2-6k+4=0

Solution for -12k^2-6k+4=0 equation:

Simplifying
-12k2 + -6k + 4 = 0

Reorder the terms:
4 + -6k + -12k2 = 0

Solving
4 + -6k + -12k2 = 0

Solving for variable 'k'.

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

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

Simplifying
2 + -3k + -6k2 = 0

Solving
2 + -3k + -6k2 = 0

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

Divide each side by '-6'.
-0.3333333333 + 0.5k + k2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + 0.5k + 0.3333333333 + k2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + 0.5k + k2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + 0.5k + k2 = 0 + 0.3333333333
0.5k + k2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
0.5k + k2 = 0.3333333333

The k term is 0.5k.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5k + 0.0625 + k2 = 0.3333333333 + 0.0625

Reorder the terms:
0.0625 + 0.5k + k2 = 0.3333333333 + 0.0625

Combine like terms: 0.3333333333 + 0.0625 = 0.3958333333
0.0625 + 0.5k + k2 = 0.3958333333

Factor a perfect square on the left side:
(k + 0.25)(k + 0.25) = 0.3958333333

Calculate the square root of the right side: 0.62915287

Break this problem into two subproblems by setting 
(k + 0.25) equal to 0.62915287 and -0.62915287.

Subproblem 1
k + 0.25 = 0.62915287

Simplifying
k + 0.25 = 0.62915287

Reorder the terms:
0.25 + k = 0.62915287

Solving
0.25 + k = 0.62915287

Solving for variable 'k'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + k = 0.62915287 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + k = 0.62915287 + -0.25
k = 0.62915287 + -0.25

Combine like terms: 0.62915287 + -0.25 = 0.37915287
k = 0.37915287

Simplifying
k = 0.37915287

Subproblem 2
k + 0.25 = -0.62915287

Simplifying
k + 0.25 = -0.62915287

Reorder the terms:
0.25 + k = -0.62915287

Solving
0.25 + k = -0.62915287

Solving for variable 'k'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + k = -0.62915287 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + k = -0.62915287 + -0.25
k = -0.62915287 + -0.25

Combine like terms: -0.62915287 + -0.25 = -0.87915287
k = -0.87915287

Simplifying
k = -0.87915287

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.37915287, -0.87915287}
Solution
k = {0.37915287, -0.87915287}