n(n+1)=12

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Solution for n(n+1)=12 equation:


Simplifying
n(n + 1) = 12

Reorder the terms:
n(1 + n) = 12
(1 * n + n * n) = 12
(1n + n2) = 12

Solving
1n + n2 = 12

Solving for variable 'n'.

Reorder the terms:
-12 + 1n + n2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + 1n + n2 = 0

Factor a trinomial.
(-4 + -1n)(3 + -1n) = 0

Subproblem 1

Set the factor '(-4 + -1n)' equal to zero and attempt to solve: Simplifying -4 + -1n = 0 Solving -4 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1n = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1n = 0 + 4 -1n = 0 + 4 Combine like terms: 0 + 4 = 4 -1n = 4 Divide each side by '-1'. n = -4 Simplifying n = -4

Subproblem 2

Set the factor '(3 + -1n)' equal to zero and attempt to solve: Simplifying 3 + -1n = 0 Solving 3 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1n = 0 + -3 -1n = 0 + -3 Combine like terms: 0 + -3 = -3 -1n = -3 Divide each side by '-1'. n = 3 Simplifying n = 3

Solution

n = {-4, 3}

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