(4k-2)(3k+6)=0

Solution for (4k-2)(3k+6)=0 equation:

Simplifying
(4k + -2)(3k + 6) = 0

Reorder the terms:
(-2 + 4k)(3k + 6) = 0

Reorder the terms:
(-2 + 4k)(6 + 3k) = 0

Multiply (-2 + 4k) * (6 + 3k)
(-2(6 + 3k) + 4k * (6 + 3k)) = 0
((6 * -2 + 3k * -2) + 4k * (6 + 3k)) = 0
((-12 + -6k) + 4k * (6 + 3k)) = 0
(-12 + -6k + (6 * 4k + 3k * 4k)) = 0
(-12 + -6k + (24k + 12k2)) = 0

Combine like terms: -6k + 24k = 18k
(-12 + 18k + 12k2) = 0

Solving
-12 + 18k + 12k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-2 + 3k + 2k2) = 0

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

Ignore the factor 6.
Subproblem 1
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
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 = {-2, 0.5}