r(r+1)=110

Solution for r(r+1)=110 equation:

Simplifying
r(r + 1) = 110

Reorder the terms:
r(1 + r) = 110
(1 * r + r * r) = 110
(1r + r2) = 110

Solving
1r + r2 = 110

Solving for variable 'r'.

Reorder the terms:
-110 + 1r + r2 = 110 + -110

Combine like terms: 110 + -110 = 0
-110 + 1r + r2 = 0

Factor a trinomial.
(-11 + -1r)(10 + -1r) = 0

Subproblem 1
Set the factor '(-11 + -1r)' equal to zero and attempt to solve:

Simplifying
-11 + -1r = 0

Solving
-11 + -1r = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1r = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1r = 0 + 11
-1r = 0 + 11

Combine like terms: 0 + 11 = 11
-1r = 11

Divide each side by '-1'.
r = -11

Simplifying
r = -11
Subproblem 2
Set the factor '(10 + -1r)' equal to zero and attempt to solve:

Simplifying
10 + -1r = 0

Solving
10 + -1r = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1r = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1r = 0 + -10
-1r = 0 + -10

Combine like terms: 0 + -10 = -10
-1r = -10

Divide each side by '-1'.
r = 10

Simplifying
r = 10
Solution
r = {-11, 10}