(r+2)(r+13)=0

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

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

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

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

Multiply (2 + r) * (13 + r)
(2(13 + r) + r(13 + r)) = 0
((13 * 2 + r * 2) + r(13 + r)) = 0
((26 + 2r) + r(13 + r)) = 0
(26 + 2r + (13 * r + r * r)) = 0
(26 + 2r + (13r + r2)) = 0

Combine like terms: 2r + 13r = 15r
(26 + 15r + r2) = 0

Solving
26 + 15r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(13 + r)(2 + r) = 0

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

Simplifying
13 + r = 0

Solving
13 + r = 0

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

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

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

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

Simplifying
r = -13
Subproblem 2
Set the factor '(2 + r)' equal to zero and attempt to solve:

Simplifying
2 + r = 0

Solving
2 + r = 0

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

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

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

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

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