(3k+3)(2k-4)=0

Solution for (3k+3)(2k-4)=0 equation:

Simplifying
(3k + 3)(2k + -4) = 0

Reorder the terms:
(3 + 3k)(2k + -4) = 0

Reorder the terms:
(3 + 3k)(-4 + 2k) = 0

Multiply (3 + 3k) * (-4 + 2k)
(3(-4 + 2k) + 3k * (-4 + 2k)) = 0
((-4 * 3 + 2k * 3) + 3k * (-4 + 2k)) = 0
((-12 + 6k) + 3k * (-4 + 2k)) = 0
(-12 + 6k + (-4 * 3k + 2k * 3k)) = 0
(-12 + 6k + (-12k + 6k2)) = 0

Combine like terms: 6k + -12k = -6k
(-12 + -6k + 6k2) = 0

Solving
-12 + -6k + 6k2 = 0

Solving for variable 'k'.

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

Factor a trinomial.
6((-1 + -1k)(2 + -1k)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-1 + -1k)' equal to zero and attempt to solve:

Simplifying
-1 + -1k = 0

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

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

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

Divide each side by '-1'.
k = -1

Simplifying
k = -1
Subproblem 2
Set the factor '(2 + -1k)' equal to zero and attempt to solve:

Simplifying
2 + -1k = 0

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

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

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

Divide each side by '-1'.
k = 2

Simplifying
k = 2
Solution
k = {-1, 2}