(x-3)(x-3)=1

Solution for (x-3)(x-3)=1 equation:

Simplifying
(x + -3)(x + -3) = 1

Reorder the terms:
(-3 + x)(x + -3) = 1

Reorder the terms:
(-3 + x)(-3 + x) = 1

Multiply (-3 + x) * (-3 + x)
(-3(-3 + x) + x(-3 + x)) = 1
((-3 * -3 + x * -3) + x(-3 + x)) = 1
((9 + -3x) + x(-3 + x)) = 1
(9 + -3x + (-3 * x + x * x)) = 1
(9 + -3x + (-3x + x2)) = 1

Combine like terms: -3x + -3x = -6x
(9 + -6x + x2) = 1

Solving
9 + -6x + x2 = 1

Solving for variable 'x'.

Reorder the terms:
9 + -1 + -6x + x2 = 1 + -1

Combine like terms: 9 + -1 = 8
8 + -6x + x2 = 1 + -1

Combine like terms: 1 + -1 = 0
8 + -6x + x2 = 0

Factor a trinomial.
(2 + -1x)(4 + -1x) = 0

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

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

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

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {2, 4}