(x-1)2-x(x-2)=1

Solution for (x-1)2-x(x-2)=1 equation:

Simplifying
(x + -1) * 2 + -1x(x + -2) = 1

Reorder the terms:
(-1 + x) * 2 + -1x(x + -2) = 1

Reorder the terms for easier multiplication:
2(-1 + x) + -1x(x + -2) = 1
(-1 * 2 + x * 2) + -1x(x + -2) = 1
(-2 + 2x) + -1x(x + -2) = 1

Reorder the terms:
-2 + 2x + -1x(-2 + x) = 1
-2 + 2x + (-2 * -1x + x * -1x) = 1
-2 + 2x + (2x + -1x2) = 1

Combine like terms: 2x + 2x = 4x
-2 + 4x + -1x2 = 1

Solving
-2 + 4x + -1x2 = 1

Solving for variable 'x'.

Reorder the terms:
-2 + -1 + 4x + -1x2 = 1 + -1

Combine like terms: -2 + -1 = -3
-3 + 4x + -1x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-3 + 4x + -1x2 = 0

Factor a trinomial.
(-3 + x)(1 + -1x) = 0

Subproblem 1
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
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
Solution
x = {3, 1}