2k(-2+8k)=0

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

Simplifying
2k(-2 + 8k) = 0
(-2 * 2k + 8k * 2k) = 0
(-4k + 16k2) = 0

Solving
-4k + 16k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '4k'.
4k(-1 + 4k) = 0

Ignore the factor 4.
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 + 4k)' equal to zero and attempt to solve:

Simplifying
-1 + 4k = 0

Solving
-1 + 4k = 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 + 4k = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 4k = 0 + 1
4k = 0 + 1

Combine like terms: 0 + 1 = 1
4k = 1

Divide each side by '4'.
k = 0.25

Simplifying
k = 0.25
Solution
k = {0, 0.25}