(x+8)(x+13)=0

Solution for (x+8)(x+13)=0 equation:

Simplifying
(x + 8)(x + 13) = 0

Reorder the terms:
(8 + x)(x + 13) = 0

Reorder the terms:
(8 + x)(13 + x) = 0

Multiply (8 + x) * (13 + x)
(8(13 + x) + x(13 + x)) = 0
((13 * 8 + x * 8) + x(13 + x)) = 0
((104 + 8x) + x(13 + x)) = 0
(104 + 8x + (13 * x + x * x)) = 0
(104 + 8x + (13x + x2)) = 0

Combine like terms: 8x + 13x = 21x
(104 + 21x + x2) = 0

Solving
104 + 21x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(13 + x)(8 + x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

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

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8
Solution
x = {-13, -8}