n^2-n=462

Solution for n^2-n=462 equation:

Simplifying
n2 + -1n = 462

Reorder the terms:
-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.
(-21 + -1n)(22 + -1n) = 0

Subproblem 1
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
Subproblem 2
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
Solution
n = {-21, 22}