(5k-9)(2k-4)=0

Solution for (5k-9)(2k-4)=0 equation:

Simplifying
(5k + -9)(2k + -4) = 0

Reorder the terms:
(-9 + 5k)(2k + -4) = 0

Reorder the terms:
(-9 + 5k)(-4 + 2k) = 0

Multiply (-9 + 5k) * (-4 + 2k)
(-9(-4 + 2k) + 5k * (-4 + 2k)) = 0
((-4 * -9 + 2k * -9) + 5k * (-4 + 2k)) = 0
((36 + -18k) + 5k * (-4 + 2k)) = 0
(36 + -18k + (-4 * 5k + 2k * 5k)) = 0
(36 + -18k + (-20k + 10k2)) = 0

Combine like terms: -18k + -20k = -38k
(36 + -38k + 10k2) = 0

Solving
36 + -38k + 10k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2'.
2(18 + -19k + 5k2) = 0

Factor a trinomial.
2((9 + -5k)(2 + -1k)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(9 + -5k)' equal to zero and attempt to solve:

Simplifying
9 + -5k = 0

Solving
9 + -5k = 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 + -5k = 0 + -9

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

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

Divide each side by '-5'.
k = 1.8

Simplifying
k = 1.8
Subproblem 2
Set the factor '(2 + -1k)' equal to zero and attempt to solve:

Simplifying
2 + -1k = 0

Solving
2 + -1k = 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 + -1k = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1k = 0 + -2
-1k = 0 + -2

Combine like terms: 0 + -2 = -2
-1k = -2

Divide each side by '-1'.
k = 2

Simplifying
k = 2
Solution
k = {1.8, 2}