6n^3-18n^2-18n=6n

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Solution for 6n^3-18n^2-18n=6n equation:


Simplifying
6n3 + -18n2 + -18n = 6n

Reorder the terms:
-18n + -18n2 + 6n3 = 6n

Solving
-18n + -18n2 + 6n3 = 6n

Solving for variable 'n'.

Reorder the terms:
-18n + -6n + -18n2 + 6n3 = 6n + -6n

Combine like terms: -18n + -6n = -24n
-24n + -18n2 + 6n3 = 6n + -6n

Combine like terms: 6n + -6n = 0
-24n + -18n2 + 6n3 = 0

Factor out the Greatest Common Factor (GCF), '6n'.
6n(-4 + -3n + n2) = 0

Factor a trinomial.
6n((-1 + -1n)(4 + -1n)) = 0

Ignore the factor 6.

Subproblem 1

Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n = 0

Subproblem 2

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

Subproblem 3

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

Solution

n = {0, -1, 4}

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