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

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


Simplifying
(2x2 + -4x)(x + -2) = 0

Reorder the terms:
(-4x + 2x2)(x + -2) = 0

Reorder the terms:
(-4x + 2x2)(-2 + x) = 0

Multiply (-4x + 2x2) * (-2 + x)
(-4x * (-2 + x) + 2x2 * (-2 + x)) = 0
((-2 * -4x + x * -4x) + 2x2 * (-2 + x)) = 0
((8x + -4x2) + 2x2 * (-2 + x)) = 0
(8x + -4x2 + (-2 * 2x2 + x * 2x2)) = 0
(8x + -4x2 + (-4x2 + 2x3)) = 0

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

Solving
8x + -8x2 + 2x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(4 + -4x + x2) = 0

Factor a trinomial.
2x((2 + -1x)(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 '(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

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, 2, 2}

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