(x+1)(x+13)=-35

Solution for (x+1)(x+13)=-35 equation:

Simplifying
(x + 1)(x + 13) = -35

Reorder the terms:
(1 + x)(x + 13) = -35

Reorder the terms:
(1 + x)(13 + x) = -35

Multiply (1 + x) * (13 + x)
(1(13 + x) + x(13 + x)) = -35
((13 * 1 + x * 1) + x(13 + x)) = -35
((13 + 1x) + x(13 + x)) = -35
(13 + 1x + (13 * x + x * x)) = -35
(13 + 1x + (13x + x2)) = -35

Combine like terms: 1x + 13x = 14x
(13 + 14x + x2) = -35

Solving
13 + 14x + x2 = -35

Solving for variable 'x'.

Reorder the terms:
13 + 35 + 14x + x2 = -35 + 35

Combine like terms: 13 + 35 = 48
48 + 14x + x2 = -35 + 35

Combine like terms: -35 + 35 = 0
48 + 14x + x2 = 0

Factor a trinomial.
(8 + x)(6 + x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Solution
x = {-8, -6}