6n^2-18n-1818=6

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Solution for 6n^2-18n-1818=6 equation:


Simplifying
6n2 + -18n + -1818 = 6

Reorder the terms:
-1818 + -18n + 6n2 = 6

Solving
-1818 + -18n + 6n2 = 6

Solving for variable 'n'.

Reorder the terms:
-1818 + -6 + -18n + 6n2 = 6 + -6

Combine like terms: -1818 + -6 = -1824
-1824 + -18n + 6n2 = 6 + -6

Combine like terms: 6 + -6 = 0
-1824 + -18n + 6n2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-304 + -3n + n2) = 0

Factor a trinomial.
6((-16 + -1n)(19 + -1n)) = 0

Ignore the factor 6.

Subproblem 1

Set the factor '(-16 + -1n)' equal to zero and attempt to solve: Simplifying -16 + -1n = 0 Solving -16 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + -1n = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -1n = 0 + 16 -1n = 0 + 16 Combine like terms: 0 + 16 = 16 -1n = 16 Divide each side by '-1'. n = -16 Simplifying n = -16

Subproblem 2

Set the factor '(19 + -1n)' equal to zero and attempt to solve: Simplifying 19 + -1n = 0 Solving 19 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + -1n = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -1n = 0 + -19 -1n = 0 + -19 Combine like terms: 0 + -19 = -19 -1n = -19 Divide each side by '-1'. n = 19 Simplifying n = 19

Solution

n = {-16, 19}

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