0=(x+13)(x-5)

Solution for 0=(x+13)(x-5) equation:

Simplifying
0 = (x + 13)(x + -5)

Reorder the terms:
0 = (13 + x)(x + -5)

Reorder the terms:
0 = (13 + x)(-5 + x)

Multiply (13 + x) * (-5 + x)
0 = (13(-5 + x) + x(-5 + x))
0 = ((-5 * 13 + x * 13) + x(-5 + x))
0 = ((-65 + 13x) + x(-5 + x))
0 = (-65 + 13x + (-5 * x + x * x))
0 = (-65 + 13x + (-5x + x2))

Combine like terms: 13x + -5x = 8x
0 = (-65 + 8x + x2)

Solving
0 = -65 + 8x + x2

Solving for variable 'x'.

Combine like terms: 0 + 65 = 65
65 + -8x + -1x2 = -65 + 8x + x2 + 65 + -8x + -1x2

Reorder the terms:
65 + -8x + -1x2 = -65 + 65 + 8x + -8x + x2 + -1x2

Combine like terms: -65 + 65 = 0
65 + -8x + -1x2 = 0 + 8x + -8x + x2 + -1x2
65 + -8x + -1x2 = 8x + -8x + x2 + -1x2

Combine like terms: 8x + -8x = 0
65 + -8x + -1x2 = 0 + x2 + -1x2
65 + -8x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
65 + -8x + -1x2 = 0

Factor a trinomial.
(5 + -1x)(13 + x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(13 + x)' equal to zero and attempt to solve:

Simplifying
13 + x = 0

Solving
13 + x = 0

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

Add '-13' to each side of the equation.
13 + -13 + x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + x = 0 + -13
x = 0 + -13

Combine like terms: 0 + -13 = -13
x = -13

Simplifying
x = -13
Solution
x = {5, -13}