x^3-3x^2+3x-1=x-1

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Solution for x^3-3x^2+3x-1=x-1 equation: 


Simplifying
x3 + -3x2 + 3x + -1 = x + -1

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

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

Add '1' to each side of the equation.
-1 + 3x + -3x2 + 1 + x3 = -1 + 1 + x

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

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

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

Solving
3x + -3x2 + x3 = x

Solving for variable 'x'.

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

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

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

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

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

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