x(2-2x)(1-2x)=0

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Solution for x(2-2x)(1-2x)=0 equation: 


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

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

Combine like terms: -4x + -2x = -6x
x(2 + -6x + 4x2) = 0
(2 * x + -6x * x + 4x2 * x) = 0
(2x + -6x2 + 4x3) = 0

Solving
2x + -6x2 + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(1 + -3x + 2x2) = 0

Factor a trinomial.
2x((1 + -2x)(1 + -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 '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

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

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {0, 0.5, 1}

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