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

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

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

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

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

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

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

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

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

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

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

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

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

Solving
-3x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-3 + x) = 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 + x)' equal to zero and attempt to solve:

Simplifying
-3 + x = 0

Solving
-3 + x = 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 + x = 0 + 3

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

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

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