n^5=n^3

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Solution for n^5=n^3 equation:


Simplifying
n5 = n3

Solving
n5 = n3

Solving for variable 'n'.

Reorder the terms:
-1n3 + n5 = n3 + -1n3

Combine like terms: n3 + -1n3 = 0
-1n3 + n5 = 0

Factor out the Greatest Common Factor (GCF), 'n3'.
n3(-1 + n2) = 0

Factor a difference between two squares.
n3((1 + n)(-1 + n)) = 0

Subproblem 1

Set the factor 'n3' equal to zero and attempt to solve: Simplifying n3 = 0 Solving n3 = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(1 + n)' equal to zero and attempt to solve: Simplifying 1 + n = 0 Solving 1 + n = 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 + n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + n = 0 + -1 n = 0 + -1 Combine like terms: 0 + -1 = -1 n = -1 Simplifying n = -1

Subproblem 3

Set the factor '(-1 + n)' equal to zero and attempt to solve: Simplifying -1 + n = 0 Solving -1 + n = 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 + n = 0 + 1 Combine like terms: -1 + 1 = 0 0 + n = 0 + 1 n = 0 + 1 Combine like terms: 0 + 1 = 1 n = 1 Simplifying n = 1

Solution

n = {-1, 1}

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