(5k-4)(3k-5)=0

Solution for (5k-4)(3k-5)=0 equation:

Simplifying
(5k + -4)(3k + -5) = 0

Reorder the terms:
(-4 + 5k)(3k + -5) = 0

Reorder the terms:
(-4 + 5k)(-5 + 3k) = 0

Multiply (-4 + 5k) * (-5 + 3k)
(-4(-5 + 3k) + 5k * (-5 + 3k)) = 0
((-5 * -4 + 3k * -4) + 5k * (-5 + 3k)) = 0
((20 + -12k) + 5k * (-5 + 3k)) = 0
(20 + -12k + (-5 * 5k + 3k * 5k)) = 0
(20 + -12k + (-25k + 15k2)) = 0

Combine like terms: -12k + -25k = -37k
(20 + -37k + 15k2) = 0

Solving
20 + -37k + 15k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(4 + -5k)(5 + -3k) = 0

Subproblem 1
Set the factor '(4 + -5k)' equal to zero and attempt to solve:

Simplifying
4 + -5k = 0

Solving
4 + -5k = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5k = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5k = 0 + -4
-5k = 0 + -4

Combine like terms: 0 + -4 = -4
-5k = -4

Divide each side by '-5'.
k = 0.8

Simplifying
k = 0.8
Subproblem 2
Set the factor '(5 + -3k)' equal to zero and attempt to solve:

Simplifying
5 + -3k = 0

Solving
5 + -3k = 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 + -3k = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3k = 0 + -5
-3k = 0 + -5

Combine like terms: 0 + -5 = -5
-3k = -5

Divide each side by '-3'.
k = 1.666666667

Simplifying
k = 1.666666667
Solution
k = {0.8, 1.666666667}