(x+1)(x+13)=0

Solution for (x+1)(x+13)=0 equation:

Simplifying
(x + 1)(x + 13) = 0

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

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

Multiply (1 + x) * (13 + x)
(1(13 + x) + x(13 + x)) = 0
((13 * 1 + x * 1) + x(13 + x)) = 0
((13 + 1x) + x(13 + x)) = 0
(13 + 1x + (13 * x + x * x)) = 0
(13 + 1x + (13x + x2)) = 0

Combine like terms: 1x + 13x = 14x
(13 + 14x + x2) = 0

Solving
13 + 14x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(13 + x)(1 + 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 '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1
Solution
x = {-13, -1}