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

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


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

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

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

Multiply (1 + -2x + 1x2) * (1 + -1x)
(1(1 + -1x) + -2x * (1 + -1x) + 1x2 * (1 + -1x)) + 1 + 1 + -1(1 + -1x) + -1(1 + -1x) + -1(1 + -1x) = 0
((1 * 1 + -1x * 1) + -2x * (1 + -1x) + 1x2 * (1 + -1x)) + 1 + 1 + -1(1 + -1x) + -1(1 + -1x) + -1(1 + -1x) = 0
((1 + -1x) + -2x * (1 + -1x) + 1x2 * (1 + -1x)) + 1 + 1 + -1(1 + -1x) + -1(1 + -1x) + -1(1 + -1x) = 0
(1 + -1x + (1 * -2x + -1x * -2x) + 1x2 * (1 + -1x)) + 1 + 1 + -1(1 + -1x) + -1(1 + -1x) + -1(1 + -1x) = 0
(1 + -1x + (-2x + 2x2) + 1x2 * (1 + -1x)) + 1 + 1 + -1(1 + -1x) + -1(1 + -1x) + -1(1 + -1x) = 0
(1 + -1x + -2x + 2x2 + (1 * 1x2 + -1x * 1x2)) + 1 + 1 + -1(1 + -1x) + -1(1 + -1x) + -1(1 + -1x) = 0
(1 + -1x + -2x + 2x2 + (1x2 + -1x3)) + 1 + 1 + -1(1 + -1x) + -1(1 + -1x) + -1(1 + -1x) = 0

Combine like terms: -1x + -2x = -3x
(1 + -3x + 2x2 + 1x2 + -1x3) + 1 + 1 + -1(1 + -1x) + -1(1 + -1x) + -1(1 + -1x) = 0

Combine like terms: 2x2 + 1x2 = 3x2
(1 + -3x + 3x2 + -1x3) + 1 + 1 + -1(1 + -1x) + -1(1 + -1x) + -1(1 + -1x) = 0
1 + -3x + 3x2 + -1x3 + 1 + 1 + (1 * -1 + -1x * -1) + -1(1 + -1x) + -1(1 + -1x) = 0
1 + -3x + 3x2 + -1x3 + 1 + 1 + (-1 + 1x) + -1(1 + -1x) + -1(1 + -1x) = 0
1 + -3x + 3x2 + -1x3 + 1 + 1 + -1 + 1x + (1 * -1 + -1x * -1) + -1(1 + -1x) = 0
1 + -3x + 3x2 + -1x3 + 1 + 1 + -1 + 1x + (-1 + 1x) + -1(1 + -1x) = 0
1 + -3x + 3x2 + -1x3 + 1 + 1 + -1 + 1x + -1 + 1x + (1 * -1 + -1x * -1) = 0
1 + -3x + 3x2 + -1x3 + 1 + 1 + -1 + 1x + -1 + 1x + (-1 + 1x) = 0

Reorder the terms:
1 + 1 + 1 + -1 + -1 + -1 + -3x + 1x + 1x + 1x + 3x2 + -1x3 = 0

Combine like terms: 1 + 1 = 2
2 + 1 + -1 + -1 + -1 + -3x + 1x + 1x + 1x + 3x2 + -1x3 = 0

Combine like terms: 2 + 1 = 3
3 + -1 + -1 + -1 + -3x + 1x + 1x + 1x + 3x2 + -1x3 = 0

Combine like terms: 3 + -1 = 2
2 + -1 + -1 + -3x + 1x + 1x + 1x + 3x2 + -1x3 = 0

Combine like terms: 2 + -1 = 1
1 + -1 + -3x + 1x + 1x + 1x + 3x2 + -1x3 = 0

Combine like terms: 1 + -1 = 0
0 + -3x + 1x + 1x + 1x + 3x2 + -1x3 = 0
-3x + 1x + 1x + 1x + 3x2 + -1x3 = 0

Combine like terms: -3x + 1x = -2x
-2x + 1x + 1x + 3x2 + -1x3 = 0

Combine like terms: -2x + 1x = -1x
-1x + 1x + 3x2 + -1x3 = 0

Combine like terms: -1x + 1x = 0
0 + 3x2 + -1x3 = 0
3x2 + -1x3 = 0

Solving
3x2 + -1x3 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0, 3}

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