(x+2)(x+13)=0

Solution for (x+2)(x+13)=0 equation:

Simplifying
(x + 2)(x + 13) = 0

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

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

Multiply (2 + x) * (13 + x)
(2(13 + x) + x(13 + x)) = 0
((13 * 2 + x * 2) + x(13 + x)) = 0
((26 + 2x) + x(13 + x)) = 0
(26 + 2x + (13 * x + x * x)) = 0
(26 + 2x + (13x + x2)) = 0

Combine like terms: 2x + 13x = 15x
(26 + 15x + x2) = 0

Solving
26 + 15x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(13 + x)(2 + 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 '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {-13, -2}