n(n+1)=182

Solution for n(n+1)=182 equation:

Simplifying
n(n + 1) = 182

Reorder the terms:
n(1 + n) = 182
(1 * n + n * n) = 182
(1n + n2) = 182

Solving
1n + n2 = 182

Solving for variable 'n'.

Reorder the terms:
-182 + 1n + n2 = 182 + -182

Combine like terms: 182 + -182 = 0
-182 + 1n + n2 = 0

Factor a trinomial.
(-14 + -1n)(13 + -1n) = 0

Subproblem 1
Set the factor '(-14 + -1n)' equal to zero and attempt to solve:

Simplifying
-14 + -1n = 0

Solving
-14 + -1n = 0

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

Add '14' to each side of the equation.
-14 + 14 + -1n = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -1n = 0 + 14
-1n = 0 + 14

Combine like terms: 0 + 14 = 14
-1n = 14

Divide each side by '-1'.
n = -14

Simplifying
n = -14
Subproblem 2
Set the factor '(13 + -1n)' equal to zero and attempt to solve:

Simplifying
13 + -1n = 0

Solving
13 + -1n = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1n = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1n = 0 + -13
-1n = 0 + -13

Combine like terms: 0 + -13 = -13
-1n = -13

Divide each side by '-1'.
n = 13

Simplifying
n = 13
Solution
n = {-14, 13}