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

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

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

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

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

Multiply (-2 + x) * (-2 + x)
(-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 = 0

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

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

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

Solving
3 + -4x + x2 = 0

Solving for variable 'x'.

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

Subproblem 1
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
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {1, 3}