8k(2k-1)=0

Solution for 8k(2k-1)=0 equation:

Simplifying
8k(2k + -1) = 0

Reorder the terms:
8k(-1 + 2k) = 0
(-1 * 8k + 2k * 8k) = 0
(-8k + 16k2) = 0

Solving
-8k + 16k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '8k'.
8k(-1 + 2k) = 0

Ignore the factor 8.
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 + 2k)' equal to zero and attempt to solve:

Simplifying
-1 + 2k = 0

Solving
-1 + 2k = 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 + 2k = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2k = 0 + 1
2k = 0 + 1

Combine like terms: 0 + 1 = 1
2k = 1

Divide each side by '2'.
k = 0.5

Simplifying
k = 0.5
Solution
k = {0, 0.5}