r(r+1)=182

Solution for r(r+1)=182 equation:

Simplifying
r(r + 1) = 182

Reorder the terms:
r(1 + r) = 182
(1 * r + r * r) = 182
(1r + r2) = 182

Solving
1r + r2 = 182

Solving for variable 'r'.

Reorder the terms:
-182 + 1r + r2 = 182 + -182

Combine like terms: 182 + -182 = 0
-182 + 1r + r2 = 0

Factor a trinomial.
(-14 + -1r)(13 + -1r) = 0

Subproblem 1
Set the factor '(-14 + -1r)' equal to zero and attempt to solve:

Simplifying
-14 + -1r = 0

Solving
-14 + -1r = 0

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

Add '14' to each side of the equation.
-14 + 14 + -1r = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -1r = 0 + 14
-1r = 0 + 14

Combine like terms: 0 + 14 = 14
-1r = 14

Divide each side by '-1'.
r = -14

Simplifying
r = -14
Subproblem 2
Set the factor '(13 + -1r)' equal to zero and attempt to solve:

Simplifying
13 + -1r = 0

Solving
13 + -1r = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1r = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1r = 0 + -13
-1r = 0 + -13

Combine like terms: 0 + -13 = -13
-1r = -13

Divide each side by '-1'.
r = 13

Simplifying
r = 13
Solution
r = {-14, 13}