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

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

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

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

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

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

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

Solving
0 = 15 + -8x + x2

Solving for variable 'x'.

Combine like terms: 0 + -15 = -15
-15 + 8x + -1x2 = 15 + -8x + x2 + -15 + 8x + -1x2

Reorder the terms:
-15 + 8x + -1x2 = 15 + -15 + -8x + 8x + x2 + -1x2

Combine like terms: 15 + -15 = 0
-15 + 8x + -1x2 = 0 + -8x + 8x + x2 + -1x2
-15 + 8x + -1x2 = -8x + 8x + x2 + -1x2

Combine like terms: -8x + 8x = 0
-15 + 8x + -1x2 = 0 + x2 + -1x2
-15 + 8x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-15 + 8x + -1x2 = 0

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

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

Simplifying
-5 + x = 0

Solving
-5 + x = 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 + x = 0 + 5

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

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

Simplifying
x = 5
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 = {5, 3}