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

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

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

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

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

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

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

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

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

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

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

Solving
-2x + x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-2 + 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 '(-2 + x)' equal to zero and attempt to solve:

Simplifying
-2 + x = 0

Solving
-2 + x = 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 + x = 0 + 2

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

Combine like terms: 0 + 2 = 2
x = 2

Simplifying
x = 2
Solution
x = {0, 2}