(3k-8)(9k-5)=0

Solution for (3k-8)(9k-5)=0 equation:

Simplifying
(3k + -8)(9k + -5) = 0

Reorder the terms:
(-8 + 3k)(9k + -5) = 0

Reorder the terms:
(-8 + 3k)(-5 + 9k) = 0

Multiply (-8 + 3k) * (-5 + 9k)
(-8(-5 + 9k) + 3k * (-5 + 9k)) = 0
((-5 * -8 + 9k * -8) + 3k * (-5 + 9k)) = 0
((40 + -72k) + 3k * (-5 + 9k)) = 0
(40 + -72k + (-5 * 3k + 9k * 3k)) = 0
(40 + -72k + (-15k + 27k2)) = 0

Combine like terms: -72k + -15k = -87k
(40 + -87k + 27k2) = 0

Solving
40 + -87k + 27k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(5 + -9k)(8 + -3k) = 0

Subproblem 1
Set the factor '(5 + -9k)' equal to zero and attempt to solve:

Simplifying
5 + -9k = 0

Solving
5 + -9k = 0

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

Add '-5' to each side of the equation.
5 + -5 + -9k = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -9k = 0 + -5
-9k = 0 + -5

Combine like terms: 0 + -5 = -5
-9k = -5

Divide each side by '-9'.
k = 0.5555555556

Simplifying
k = 0.5555555556
Subproblem 2
Set the factor '(8 + -3k)' equal to zero and attempt to solve:

Simplifying
8 + -3k = 0

Solving
8 + -3k = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3k = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3k = 0 + -8
-3k = 0 + -8

Combine like terms: 0 + -8 = -8
-3k = -8

Divide each side by '-3'.
k = 2.666666667

Simplifying
k = 2.666666667
Solution
k = {0.5555555556, 2.666666667}