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}