(r+4)(r+36)=0

Solution for (r+4)(r+36)=0 equation:

Simplifying
(r + 4)(r + 36) = 0

Reorder the terms:
(4 + r)(r + 36) = 0

Reorder the terms:
(4 + r)(36 + r) = 0

Multiply (4 + r) * (36 + r)
(4(36 + r) + r(36 + r)) = 0
((36 * 4 + r * 4) + r(36 + r)) = 0
((144 + 4r) + r(36 + r)) = 0
(144 + 4r + (36 * r + r * r)) = 0
(144 + 4r + (36r + r2)) = 0

Combine like terms: 4r + 36r = 40r
(144 + 40r + r2) = 0

Solving
144 + 40r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(36 + r)(4 + r) = 0

Subproblem 1
Set the factor '(36 + r)' equal to zero and attempt to solve:

Simplifying
36 + r = 0

Solving
36 + r = 0

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

Add '-36' to each side of the equation.
36 + -36 + r = 0 + -36

Combine like terms: 36 + -36 = 0
0 + r = 0 + -36
r = 0 + -36

Combine like terms: 0 + -36 = -36
r = -36

Simplifying
r = -36
Subproblem 2
Set the factor '(4 + r)' equal to zero and attempt to solve:

Simplifying
4 + r = 0

Solving
4 + r = 0

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

Add '-4' to each side of the equation.
4 + -4 + r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + r = 0 + -4
r = 0 + -4

Combine like terms: 0 + -4 = -4
r = -4

Simplifying
r = -4
Solution
r = {-36, -4}