(2+9k)(3-4k)=0

Solution for (2+9k)(3-4k)=0 equation:

Simplifying
(2 + 9k)(3 + -4k) = 0

Multiply (2 + 9k) * (3 + -4k)
(2(3 + -4k) + 9k * (3 + -4k)) = 0
((3 * 2 + -4k * 2) + 9k * (3 + -4k)) = 0
((6 + -8k) + 9k * (3 + -4k)) = 0
(6 + -8k + (3 * 9k + -4k * 9k)) = 0
(6 + -8k + (27k + -36k2)) = 0

Combine like terms: -8k + 27k = 19k
(6 + 19k + -36k2) = 0

Solving
6 + 19k + -36k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(3 + -4k)(2 + 9k) = 0

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

Simplifying
3 + -4k = 0

Solving
3 + -4k = 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 + -4k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4k = 0 + -3
-4k = 0 + -3

Combine like terms: 0 + -3 = -3
-4k = -3

Divide each side by '-4'.
k = 0.75

Simplifying
k = 0.75
Subproblem 2
Set the factor '(2 + 9k)' equal to zero and attempt to solve:

Simplifying
2 + 9k = 0

Solving
2 + 9k = 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 + 9k = 0 + -2

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

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

Divide each side by '9'.
k = -0.2222222222

Simplifying
k = -0.2222222222
Solution
k = {0.75, -0.2222222222}