r(r+1)=462

Solution for r(r+1)=462 equation:

Simplifying
r(r + 1) = 462

Reorder the terms:
r(1 + r) = 462
(1 * r + r * r) = 462
(1r + r2) = 462

Solving
1r + r2 = 462

Solving for variable 'r'.

Reorder the terms:
-462 + 1r + r2 = 462 + -462

Combine like terms: 462 + -462 = 0
-462 + 1r + r2 = 0

Factor a trinomial.
(-22 + -1r)(21 + -1r) = 0

Subproblem 1
Set the factor '(-22 + -1r)' equal to zero and attempt to solve:

Simplifying
-22 + -1r = 0

Solving
-22 + -1r = 0

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

Add '22' to each side of the equation.
-22 + 22 + -1r = 0 + 22

Combine like terms: -22 + 22 = 0
0 + -1r = 0 + 22
-1r = 0 + 22

Combine like terms: 0 + 22 = 22
-1r = 22

Divide each side by '-1'.
r = -22

Simplifying
r = -22
Subproblem 2
Set the factor '(21 + -1r)' equal to zero and attempt to solve:

Simplifying
21 + -1r = 0

Solving
21 + -1r = 0

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

Add '-21' to each side of the equation.
21 + -21 + -1r = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -1r = 0 + -21
-1r = 0 + -21

Combine like terms: 0 + -21 = -21
-1r = -21

Divide each side by '-1'.
r = 21

Simplifying
r = 21
Solution
r = {-22, 21}