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

Solution for 0=(x-2)(x-2)-1 equation:

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

Reorder the terms:
0 = (-2 + x)(x + -2) + -1

Reorder the terms:
0 = (-2 + x)(-2 + x) + -1

Multiply (-2 + x) * (-2 + x)
0 = (-2(-2 + x) + x(-2 + x)) + -1
0 = ((-2 * -2 + x * -2) + x(-2 + x)) + -1
0 = ((4 + -2x) + x(-2 + x)) + -1
0 = (4 + -2x + (-2 * x + x * x)) + -1
0 = (4 + -2x + (-2x + x2)) + -1

Combine like terms: -2x + -2x = -4x
0 = (4 + -4x + x2) + -1

Reorder the terms:
0 = 4 + -1 + -4x + x2

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

Solving
0 = 3 + -4x + x2

Solving for variable 'x'.

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

Reorder the terms:
-3 + 4x + -1x2 = 3 + -3 + -4x + 4x + x2 + -1x2

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

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

Combine like terms: x2 + -1x2 = 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}