(r+6)(r+5)=0

Solution for (r+6)(r+5)=0 equation:

Simplifying
(r + 6)(r + 5) = 0

Reorder the terms:
(6 + r)(r + 5) = 0

Reorder the terms:
(6 + r)(5 + r) = 0

Multiply (6 + r) * (5 + r)
(6(5 + r) + r(5 + r)) = 0
((5 * 6 + r * 6) + r(5 + r)) = 0
((30 + 6r) + r(5 + r)) = 0
(30 + 6r + (5 * r + r * r)) = 0
(30 + 6r + (5r + r2)) = 0

Combine like terms: 6r + 5r = 11r
(30 + 11r + r2) = 0

Solving
30 + 11r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(6 + r)(5 + r) = 0

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

Simplifying
6 + r = 0

Solving
6 + r = 0

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

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

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

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

Simplifying
r = -6
Subproblem 2
Set the factor '(5 + r)' equal to zero and attempt to solve:

Simplifying
5 + r = 0

Solving
5 + r = 0

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

Add '-5' to each side of the equation.
5 + -5 + r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + r = 0 + -5
r = 0 + -5

Combine like terms: 0 + -5 = -5
r = -5

Simplifying
r = -5
Solution
r = {-6, -5}