(n-1)(n)=182

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

Simplifying
(n + -1)(n) = 182

Reorder the terms:
(-1 + n)(n) = 182

Reorder the terms for easier multiplication:
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.
(-13 + -1n)(14 + -1n) = 0

Subproblem 1
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
Subproblem 2
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
Solution
n = {-13, 14}