n(n+1)=1122

Solution for n(n+1)=1122 equation:

Simplifying
n(n + 1) = 1122

Reorder the terms:
n(1 + n) = 1122
(1 * n + n * n) = 1122
(1n + n2) = 1122

Solving
1n + n2 = 1122

Solving for variable 'n'.

Reorder the terms:
-1122 + 1n + n2 = 1122 + -1122

Combine like terms: 1122 + -1122 = 0
-1122 + 1n + n2 = 0

Factor a trinomial.
(-34 + -1n)(33 + -1n) = 0

Subproblem 1
Set the factor '(-34 + -1n)' equal to zero and attempt to solve:

Simplifying
-34 + -1n = 0

Solving
-34 + -1n = 0

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

Add '34' to each side of the equation.
-34 + 34 + -1n = 0 + 34

Combine like terms: -34 + 34 = 0
0 + -1n = 0 + 34
-1n = 0 + 34

Combine like terms: 0 + 34 = 34
-1n = 34

Divide each side by '-1'.
n = -34

Simplifying
n = -34
Subproblem 2
Set the factor '(33 + -1n)' equal to zero and attempt to solve:

Simplifying
33 + -1n = 0

Solving
33 + -1n = 0

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

Add '-33' to each side of the equation.
33 + -33 + -1n = 0 + -33

Combine like terms: 33 + -33 = 0
0 + -1n = 0 + -33
-1n = 0 + -33

Combine like terms: 0 + -33 = -33
-1n = -33

Divide each side by '-1'.
n = 33

Simplifying
n = 33
Solution
n = {-34, 33}