2k(3-k)x(k-3)=0

Solution for 2k(3-k)x(k-3)=0 equation:

Simplifying
2k(3 + -1k) * x(k + -3) = 0

Reorder the terms:
2k(3 + -1k) * x(-3 + k) = 0

Reorder the terms for easier multiplication:
2k * x(3 + -1k)(-3 + k) = 0

Multiply k * x
2kx(3 + -1k)(-3 + k) = 0

Multiply (3 + -1k) * (-3 + k)
2kx(3(-3 + k) + -1k * (-3 + k)) = 0
2kx((-3 * 3 + k * 3) + -1k * (-3 + k)) = 0
2kx((-9 + 3k) + -1k * (-3 + k)) = 0
2kx(-9 + 3k + (-3 * -1k + k * -1k)) = 0
2kx(-9 + 3k + (3k + -1k2)) = 0

Combine like terms: 3k + 3k = 6k
2kx(-9 + 6k + -1k2) = 0
(-9 * 2kx + 6k * 2kx + -1k2 * 2kx) = 0
(-18kx + 12k2x + -2k3x) = 0

Solving
-18kx + 12k2x + -2k3x = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2kx'.
2kx(-9 + 6k + -1k2) = 0

Factor a trinomial.
2kx((-3 + k)(3 + -1k)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'kx' equal to zero and attempt to solve:

Simplifying
kx = 0

Solving
kx = 0

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

Simplifying
kx = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(-3 + k)' equal to zero and attempt to solve:

Simplifying
-3 + k = 0

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

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

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

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

Simplifying
3 + -1k = 0

Solving
3 + -1k = 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 + -1k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1k = 0 + -3
-1k = 0 + -3

Combine like terms: 0 + -3 = -3
-1k = -3

Divide each side by '-1'.
k = 3

Simplifying
k = 3
Solution
k = {3, 3}