(3k+6)(2k+12)=0

Solution for (3k+6)(2k+12)=0 equation:

Simplifying
(3k + 6)(2k + 12) = 0

Reorder the terms:
(6 + 3k)(2k + 12) = 0

Reorder the terms:
(6 + 3k)(12 + 2k) = 0

Multiply (6 + 3k) * (12 + 2k)
(6(12 + 2k) + 3k * (12 + 2k)) = 0
((12 * 6 + 2k * 6) + 3k * (12 + 2k)) = 0
((72 + 12k) + 3k * (12 + 2k)) = 0
(72 + 12k + (12 * 3k + 2k * 3k)) = 0
(72 + 12k + (36k + 6k2)) = 0

Combine like terms: 12k + 36k = 48k
(72 + 48k + 6k2) = 0

Solving
72 + 48k + 6k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '6'.
6(12 + 8k + k2) = 0

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

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

Simplifying
6 + k = 0

Solving
6 + k = 0

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

Add '-6' to each side of the equation.
6 + -6 + k = 0 + -6

Combine like terms: 6 + -6 = 0
0 + k = 0 + -6
k = 0 + -6

Combine like terms: 0 + -6 = -6
k = -6

Simplifying
k = -6
Subproblem 2
Set the factor '(2 + k)' equal to zero and attempt to solve:

Simplifying
2 + k = 0

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

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

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

Simplifying
k = -2
Solution
k = {-6, -2}