r(r+1)=132

Solution for r(r+1)=132 equation:

Simplifying
r(r + 1) = 132

Reorder the terms:
r(1 + r) = 132
(1 * r + r * r) = 132
(1r + r2) = 132

Solving
1r + r2 = 132

Solving for variable 'r'.

Reorder the terms:
-132 + 1r + r2 = 132 + -132

Combine like terms: 132 + -132 = 0
-132 + 1r + r2 = 0

Factor a trinomial.
(-12 + -1r)(11 + -1r) = 0

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

Simplifying
-12 + -1r = 0

Solving
-12 + -1r = 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 + -1r = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1r = 0 + 12
-1r = 0 + 12

Combine like terms: 0 + 12 = 12
-1r = 12

Divide each side by '-1'.
r = -12

Simplifying
r = -12
Subproblem 2
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
Solution
r = {-12, 11}