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

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

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

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

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

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

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

Solving
3 + -4x + x2 = -1

Solving for variable 'x'.

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

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

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

Factor a trinomial.
(2 + -1x)(2 + -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 '(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
Solution
x = {2, 2}