3(8k-1)(3k+1)=0

Solution for 3(8k-1)(3k+1)=0 equation:

Simplifying
3(8k + -1)(3k + 1) = 0

Reorder the terms:
3(-1 + 8k)(3k + 1) = 0

Reorder the terms:
3(-1 + 8k)(1 + 3k) = 0

Multiply (-1 + 8k) * (1 + 3k)
3(-1(1 + 3k) + 8k * (1 + 3k)) = 0
3((1 * -1 + 3k * -1) + 8k * (1 + 3k)) = 0
3((-1 + -3k) + 8k * (1 + 3k)) = 0
3(-1 + -3k + (1 * 8k + 3k * 8k)) = 0
3(-1 + -3k + (8k + 24k2)) = 0

Combine like terms: -3k + 8k = 5k
3(-1 + 5k + 24k2) = 0
(-1 * 3 + 5k * 3 + 24k2 * 3) = 0
(-3 + 15k + 72k2) = 0

Solving
-3 + 15k + 72k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + 5k + 24k2) = 0

Factor a trinomial.
3((-1 + -3k)(1 + -8k)) = 0

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
Set the factor '(1 + -8k)' equal to zero and attempt to solve:

Simplifying
1 + -8k = 0

Solving
1 + -8k = 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 + -8k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -8k = 0 + -1
-8k = 0 + -1

Combine like terms: 0 + -1 = -1
-8k = -1

Divide each side by '-8'.
k = 0.125

Simplifying
k = 0.125
Solution
k = {-0.3333333333, 0.125}