(x-1)(x-3)=0

Solution for (x-1)(x-3)=0 equation:

Simplifying
(x + -1)(x + -3) = 0

Reorder the terms:
(-1 + x)(x + -3) = 0

Reorder the terms:
(-1 + x)(-3 + x) = 0

Multiply (-1 + x) * (-3 + x)
(-1(-3 + x) + x(-3 + x)) = 0
((-3 * -1 + x * -1) + x(-3 + x)) = 0
((3 + -1x) + x(-3 + x)) = 0
(3 + -1x + (-3 * x + x * x)) = 0
(3 + -1x + (-3x + x2)) = 0

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