81r^3-16r=0

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Solution for 81r^3-16r=0 equation:


Simplifying
81r3 + -16r = 0

Reorder the terms:
-16r + 81r3 = 0

Solving
-16r + 81r3 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r'.
r(-16 + 81r2) = 0

Factor a difference between two squares.
r((4 + 9r)(-4 + 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 '(4 + 9r)' equal to zero and attempt to solve: Simplifying 4 + 9r = 0 Solving 4 + 9r = 0 Move all terms containing r to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 9r = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 9r = 0 + -4 9r = 0 + -4 Combine like terms: 0 + -4 = -4 9r = -4 Divide each side by '9'. r = -0.4444444444 Simplifying r = -0.4444444444

Subproblem 3

Set the factor '(-4 + 9r)' equal to zero and attempt to solve: Simplifying -4 + 9r = 0 Solving -4 + 9r = 0 Move all terms containing r to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + 9r = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 9r = 0 + 4 9r = 0 + 4 Combine like terms: 0 + 4 = 4 9r = 4 Divide each side by '9'. r = 0.4444444444 Simplifying r = 0.4444444444

Solution

r = {0, -0.4444444444, 0.4444444444}

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