6k^2-2k=0

Solution for 6k^2-2k=0 equation:

Simplifying
6k2 + -2k = 0

Reorder the terms:
-2k + 6k2 = 0

Solving
-2k + 6k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2k'.
2k(-1 + 3k) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'k' equal to zero and attempt to solve:

Simplifying
k = 0

Solving
k = 0

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

Simplifying
k = 0
Subproblem 2
Set the factor '(-1 + 3k)' equal to zero and attempt to solve:

Simplifying
-1 + 3k = 0

Solving
-1 + 3k = 0

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

Add '1' to each side of the equation.
-1 + 1 + 3k = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 3k = 0 + 1
3k = 0 + 1

Combine like terms: 0 + 1 = 1
3k = 1

Divide each side by '3'.
k = 0.3333333333

Simplifying
k = 0.3333333333
Solution
k = {0, 0.3333333333}