n^3-81n=0

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Solution for n^3-81n=0 equation:


Simplifying
n3 + -81n = 0

Reorder the terms:
-81n + n3 = 0

Solving
-81n + n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), 'n'.
n(-81 + n2) = 0

Factor a difference between two squares.
n((9 + n)(-9 + n)) = 0

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 '(9 + n)' equal to zero and attempt to solve: Simplifying 9 + n = 0 Solving 9 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + n = 0 + -9 Combine like terms: 9 + -9 = 0 0 + n = 0 + -9 n = 0 + -9 Combine like terms: 0 + -9 = -9 n = -9 Simplifying n = -9

Subproblem 3

Set the factor '(-9 + n)' equal to zero and attempt to solve: Simplifying -9 + n = 0 Solving -9 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + n = 0 + 9 Combine like terms: -9 + 9 = 0 0 + n = 0 + 9 n = 0 + 9 Combine like terms: 0 + 9 = 9 n = 9 Simplifying n = 9

Solution

n = {0, -9, 9}

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