2(3k-2)(2k+1)=0

Solution for 2(3k-2)(2k+1)=0 equation:

Simplifying
2(3k + -2)(2k + 1) = 0

Reorder the terms:
2(-2 + 3k)(2k + 1) = 0

Reorder the terms:
2(-2 + 3k)(1 + 2k) = 0

Multiply (-2 + 3k) * (1 + 2k)
2(-2(1 + 2k) + 3k * (1 + 2k)) = 0
2((1 * -2 + 2k * -2) + 3k * (1 + 2k)) = 0
2((-2 + -4k) + 3k * (1 + 2k)) = 0
2(-2 + -4k + (1 * 3k + 2k * 3k)) = 0
2(-2 + -4k + (3k + 6k2)) = 0

Combine like terms: -4k + 3k = -1k
2(-2 + -1k + 6k2) = 0
(-2 * 2 + -1k * 2 + 6k2 * 2) = 0
(-4 + -2k + 12k2) = 0

Solving
-4 + -2k + 12k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + -1k + 6k2) = 0

Factor a trinomial.
2((-1 + -2k)(2 + -3k)) = 0

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

Simplifying
2 + -3k = 0

Solving
2 + -3k = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3k = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3k = 0 + -2
-3k = 0 + -2

Combine like terms: 0 + -2 = -2
-3k = -2

Divide each side by '-3'.
k = 0.6666666667

Simplifying
k = 0.6666666667
Solution
k = {-0.5, 0.6666666667}