r(r+17)=-60

Solution for r(r+17)=-60 equation:

Simplifying
r(r + 17) = -60

Reorder the terms:
r(17 + r) = -60
(17 * r + r * r) = -60
(17r + r2) = -60

Solving
17r + r2 = -60

Solving for variable 'r'.

Reorder the terms:
60 + 17r + r2 = -60 + 60

Combine like terms: -60 + 60 = 0
60 + 17r + r2 = 0

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

Subproblem 1
Set the factor '(12 + r)' equal to zero and attempt to solve:

Simplifying
12 + r = 0

Solving
12 + r = 0

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

Add '-12' to each side of the equation.
12 + -12 + r = 0 + -12

Combine like terms: 12 + -12 = 0
0 + r = 0 + -12
r = 0 + -12

Combine like terms: 0 + -12 = -12
r = -12

Simplifying
r = -12
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 = {-12, -5}