r(30r+61)=-30

Solution for r(30r+61)=-30 equation:

Simplifying
r(30r + 61) = -30

Reorder the terms:
r(61 + 30r) = -30
(61 * r + 30r * r) = -30
(61r + 30r2) = -30

Solving
61r + 30r2 = -30

Solving for variable 'r'.

Reorder the terms:
30 + 61r + 30r2 = -30 + 30

Combine like terms: -30 + 30 = 0
30 + 61r + 30r2 = 0

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

Subproblem 1
Set the factor '(6 + 5r)' equal to zero and attempt to solve:

Simplifying
6 + 5r = 0

Solving
6 + 5r = 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 + 5r = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5r = 0 + -6
5r = 0 + -6

Combine like terms: 0 + -6 = -6
5r = -6

Divide each side by '5'.
r = -1.2

Simplifying
r = -1.2
Subproblem 2
Set the factor '(5 + 6r)' equal to zero and attempt to solve:

Simplifying
5 + 6r = 0

Solving
5 + 6r = 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 + 6r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 6r = 0 + -5
6r = 0 + -5

Combine like terms: 0 + -5 = -5
6r = -5

Divide each side by '6'.
r = -0.8333333333

Simplifying
r = -0.8333333333
Solution
r = {-1.2, -0.8333333333}