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.
(-32 + -1n)(31 + -1n) = 0

Subproblem 1
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
Subproblem 2
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
Solution
n = {-32, 31}