(2k+9)(3k+2)=0

Solution for (2k+9)(3k+2)=0 equation:

Simplifying
(2k + 9)(3k + 2) = 0

Reorder the terms:
(9 + 2k)(3k + 2) = 0

Reorder the terms:
(9 + 2k)(2 + 3k) = 0

Multiply (9 + 2k) * (2 + 3k)
(9(2 + 3k) + 2k * (2 + 3k)) = 0
((2 * 9 + 3k * 9) + 2k * (2 + 3k)) = 0
((18 + 27k) + 2k * (2 + 3k)) = 0
(18 + 27k + (2 * 2k + 3k * 2k)) = 0
(18 + 27k + (4k + 6k2)) = 0

Combine like terms: 27k + 4k = 31k
(18 + 31k + 6k2) = 0

Solving
18 + 31k + 6k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(9 + 2k)(2 + 3k) = 0

Subproblem 1
Set the factor '(9 + 2k)' equal to zero and attempt to solve:

Simplifying
9 + 2k = 0

Solving
9 + 2k = 0

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

Add '-9' to each side of the equation.
9 + -9 + 2k = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 2k = 0 + -9
2k = 0 + -9

Combine like terms: 0 + -9 = -9
2k = -9

Divide each side by '2'.
k = -4.5

Simplifying
k = -4.5
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 = {-4.5, -0.6666666667}