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

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

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

Solving for variable 'x'.

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

Factor a trinomial.
2x((-1 + -1x)(1 + -2x)) = 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 + -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
Subproblem 3
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
Solution
x = {0, -1, 0.5}