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

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

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

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

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

Multiply (2 + 3k) * (3 + 2k)
-4(2(3 + 2k) + 3k * (3 + 2k)) = 0
-4((3 * 2 + 2k * 2) + 3k * (3 + 2k)) = 0
-4((6 + 4k) + 3k * (3 + 2k)) = 0
-4(6 + 4k + (3 * 3k + 2k * 3k)) = 0
-4(6 + 4k + (9k + 6k2)) = 0

Combine like terms: 4k + 9k = 13k
-4(6 + 13k + 6k2) = 0
(6 * -4 + 13k * -4 + 6k2 * -4) = 0
(-24 + -52k + -24k2) = 0

Solving
-24 + -52k + -24k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '-4'.
-4(6 + 13k + 6k2) = 0

Factor a trinomial.
-4((3 + 2k)(2 + 3k)) = 0

Ignore the factor -4.
Subproblem 1
Set the factor '(3 + 2k)' equal to zero and attempt to solve:

Simplifying
3 + 2k = 0

Solving
3 + 2k = 0

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

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

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

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

Divide each side by '2'.
k = -1.5

Simplifying
k = -1.5
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 = {-1.5, -0.6666666667}