(x-3)*(x-5)=0

Solution for (x-3)*(x-5)=0 equation:

Simplifying
(x + -3)(x + -5) = 0

Reorder the terms:
(-3 + x)(x + -5) = 0

Reorder the terms:
(-3 + x)(-5 + x) = 0

Multiply (-3 + x) * (-5 + x)
(-3(-5 + x) + x(-5 + x)) = 0
((-5 * -3 + x * -3) + x(-5 + x)) = 0
((15 + -3x) + x(-5 + x)) = 0
(15 + -3x + (-5 * x + x * x)) = 0
(15 + -3x + (-5x + x2)) = 0

Combine like terms: -3x + -5x = -8x
(15 + -8x + x2) = 0

Solving
15 + -8x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + -1x)(5 + -1x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {3, 5}