x(x-1)(1-x)=

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

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

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

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

Combine like terms: 1x + 1x = 2x
x(-1 + 2x + -1x2) = 0
(-1 * x + 2x * x + -1x2 * x) = 0
(-1x + 2x2 + -1x3) = 0

Solving
-1x + 2x2 + -1x3 = 0

Solving for variable 'x'.

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

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

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 + x)' equal to zero and attempt to solve:

Simplifying
-1 + x = 0

Solving
-1 + x = 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 + x = 0 + 1

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

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

Simplifying
x = 1
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, 1, 1}