r(r+11)=-30

Solution for r(r+11)=-30 equation:

Simplifying
r(r + 11) = -30

Reorder the terms:
r(11 + r) = -30
(11 * r + r * r) = -30
(11r + r2) = -30

Solving
11r + r2 = -30

Solving for variable 'r'.

Reorder the terms:
30 + 11r + r2 = -30 + 30

Combine like terms: -30 + 30 = 0
30 + 11r + r2 = 0

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}