n(n+1)=462

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

Simplifying
n(n + 1) = 462

Reorder the terms:
n(1 + n) = 462
(1 * n + n * n) = 462
(1n + n2) = 462

Solving
1n + n2 = 462

Solving for variable 'n'.

Reorder the terms:
-462 + 1n + n2 = 462 + -462

Combine like terms: 462 + -462 = 0
-462 + 1n + n2 = 0

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

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

Simplifying
-22 + -1n = 0

Solving
-22 + -1n = 0

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

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

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

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

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

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

Simplifying
21 + -1n = 0

Solving
21 + -1n = 0

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

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

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

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

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

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