81r^3-25r=0

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Solution for 81r^3-25r=0 equation:


Simplifying
81r3 + -25r = 0

Reorder the terms:
-25r + 81r3 = 0

Solving
-25r + 81r3 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r'.
r(-25 + 81r2) = 0

Factor a difference between two squares.
r((5 + 9r)(-5 + 9r)) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(5 + 9r)' equal to zero and attempt to solve: Simplifying 5 + 9r = 0 Solving 5 + 9r = 0 Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 9r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 9r = 0 + -5 9r = 0 + -5 Combine like terms: 0 + -5 = -5 9r = -5 Divide each side by '9'. r = -0.5555555556 Simplifying r = -0.5555555556

Subproblem 3

Set the factor '(-5 + 9r)' equal to zero and attempt to solve: Simplifying -5 + 9r = 0 Solving -5 + 9r = 0 Move all terms containing r to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + 9r = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 9r = 0 + 5 9r = 0 + 5 Combine like terms: 0 + 5 = 5 9r = 5 Divide each side by '9'. r = 0.5555555556 Simplifying r = 0.5555555556

Solution

r = {0, -0.5555555556, 0.5555555556}

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