r(r+1)=240

Solution for r(r+1)=240 equation:

Simplifying
r(r + 1) = 240

Reorder the terms:
r(1 + r) = 240
(1 * r + r * r) = 240
(1r + r2) = 240

Solving
1r + r2 = 240

Solving for variable 'r'.

Reorder the terms:
-240 + 1r + r2 = 240 + -240

Combine like terms: 240 + -240 = 0
-240 + 1r + r2 = 0

Factor a trinomial.
(-16 + -1r)(15 + -1r) = 0

Subproblem 1
Set the factor '(-16 + -1r)' equal to zero and attempt to solve:

Simplifying
-16 + -1r = 0

Solving
-16 + -1r = 0

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

Add '16' to each side of the equation.
-16 + 16 + -1r = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1r = 0 + 16
-1r = 0 + 16

Combine like terms: 0 + 16 = 16
-1r = 16

Divide each side by '-1'.
r = -16

Simplifying
r = -16
Subproblem 2
Set the factor '(15 + -1r)' equal to zero and attempt to solve:

Simplifying
15 + -1r = 0

Solving
15 + -1r = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1r = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1r = 0 + -15
-1r = 0 + -15

Combine like terms: 0 + -15 = -15
-1r = -15

Divide each side by '-1'.
r = 15

Simplifying
r = 15
Solution
r = {-16, 15}