x(2x-4)(4-x)=0

Solution for x(2x-4)(4-x)=0 equation:

Simplifying
x(2x + -4)(4 + -1x) = 0

Reorder the terms:
x(-4 + 2x)(4 + -1x) = 0

Multiply (-4 + 2x) * (4 + -1x)
x(-4(4 + -1x) + 2x * (4 + -1x)) = 0
x((4 * -4 + -1x * -4) + 2x * (4 + -1x)) = 0
x((-16 + 4x) + 2x * (4 + -1x)) = 0
x(-16 + 4x + (4 * 2x + -1x * 2x)) = 0
x(-16 + 4x + (8x + -2x2)) = 0

Combine like terms: 4x + 8x = 12x
x(-16 + 12x + -2x2) = 0
(-16 * x + 12x * x + -2x2 * x) = 0
(-16x + 12x2 + -2x3) = 0

Solving
-16x + 12x2 + -2x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-8 + 6x + -1x2) = 0

Factor a trinomial.
2x((-4 + x)(2 + -1x)) = 0

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

Solving
-4 + x = 0

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

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

Combine like terms: -4 + 4 = 0
0 + x = 0 + 4
x = 0 + 4

Combine like terms: 0 + 4 = 4
x = 4

Simplifying
x = 4
Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

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

Simplifying
x = 2
Solution
x = {0, 4, 2}