Simplifying
50k2 + -20k + -6 = 0

Reorder the terms:
-6 + -20k + 50k2 = 0

Solving
-6 + -20k + 50k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -10k + 25k2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -10k + 25k2)' equal to zero and attempt to solve:

Simplifying
-3 + -10k + 25k2 = 0

Solving
-3 + -10k + 25k2 = 0

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

Divide each side by '25'.
-0.12 + -0.4k + k2 = 0

Move the constant term to the right:

Add '0.12' to each side of the equation.
-0.12 + -0.4k + 0.12 + k2 = 0 + 0.12

Reorder the terms:
-0.12 + 0.12 + -0.4k + k2 = 0 + 0.12

Combine like terms: -0.12 + 0.12 = 0.00
0.00 + -0.4k + k2 = 0 + 0.12
-0.4k + k2 = 0 + 0.12

Combine like terms: 0 + 0.12 = 0.12
-0.4k + k2 = 0.12

The k term is -0.4k.  Take half its coefficient (-0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
-0.4k + 0.04 + k2 = 0.12 + 0.04

Reorder the terms:
0.04 + -0.4k + k2 = 0.12 + 0.04

Combine like terms: 0.12 + 0.04 = 0.16
0.04 + -0.4k + k2 = 0.16

Factor a perfect square on the left side:
(k + -0.2)(k + -0.2) = 0.16

Calculate the square root of the right side: 0.4

Break this problem into two subproblems by setting 
(k + -0.2) equal to 0.4 and -0.4.

Subproblem 1
k + -0.2 = 0.4

Simplifying
k + -0.2 = 0.4

Reorder the terms:
-0.2 + k = 0.4

Solving
-0.2 + k = 0.4

Solving for variable 'k'.

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

Add '0.2' to each side of the equation.
-0.2 + 0.2 + k = 0.4 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + k = 0.4 + 0.2
k = 0.4 + 0.2

Combine like terms: 0.4 + 0.2 = 0.6
k = 0.6

Simplifying
k = 0.6

Subproblem 2
k + -0.2 = -0.4

Simplifying
k + -0.2 = -0.4

Reorder the terms:
-0.2 + k = -0.4

Solving
-0.2 + k = -0.4

Solving for variable 'k'.

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

Add '0.2' to each side of the equation.
-0.2 + 0.2 + k = -0.4 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + k = -0.4 + 0.2
k = -0.4 + 0.2

Combine like terms: -0.4 + 0.2 = -0.2
k = -0.2

Simplifying
k = -0.2

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.6, -0.2}
Solution
k = {0.6, -0.2}