n(n-1)=992

Solution for n(n-1)=992 equation:

Simplifying
n(n + -1) = 992

Reorder the terms:
n(-1 + n) = 992
(-1 * n + n * n) = 992
(-1n + n2) = 992

Solving
-1n + n2 = 992

Solving for variable 'n'.

Reorder the terms:
-992 + -1n + n2 = 992 + -992

Combine like terms: 992 + -992 = 0
-992 + -1n + n2 = 0

Factor a trinomial.
(-31 + -1n)(32 + -1n) = 0

Subproblem 1
Set the factor '(-31 + -1n)' equal to zero and attempt to solve:

Simplifying
-31 + -1n = 0

Solving
-31 + -1n = 0

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

Add '31' to each side of the equation.
-31 + 31 + -1n = 0 + 31

Combine like terms: -31 + 31 = 0
0 + -1n = 0 + 31
-1n = 0 + 31

Combine like terms: 0 + 31 = 31
-1n = 31

Divide each side by '-1'.
n = -31

Simplifying
n = -31
Subproblem 2
Set the factor '(32 + -1n)' equal to zero and attempt to solve:

Simplifying
32 + -1n = 0

Solving
32 + -1n = 0

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

Add '-32' to each side of the equation.
32 + -32 + -1n = 0 + -32

Combine like terms: 32 + -32 = 0
0 + -1n = 0 + -32
-1n = 0 + -32

Combine like terms: 0 + -32 = -32
-1n = -32

Divide each side by '-1'.
n = 32

Simplifying
n = 32
Solution
n = {-31, 32}