x^2-2x-1=x-1

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

Simplifying
x2 + -2x + -1 = x + -1

Reorder the terms:
-1 + -2x + x2 = x + -1

Reorder the terms:
-1 + -2x + x2 = -1 + x

Add '1' to each side of the equation.
-1 + -2x + 1 + x2 = -1 + 1 + x

Reorder the terms:
-1 + 1 + -2x + x2 = -1 + 1 + x

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

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

Solving
-2x + x2 = x

Solving for variable 'x'.

Reorder the terms:
-2x + -1x + x2 = x + -1x

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

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

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