n(n+1)=182

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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}

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