81x^3-4xy^2=0

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Solution for 81x^3-4xy^2=0 equation: 


Simplifying
81x3 + -4xy2 = 0

Reorder the terms:
-4xy2 + 81x3 = 0

Solving
-4xy2 + 81x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-4y2 + 81x2) = 0

Factor a difference between two squares.
x((2y + 9x)(-2y + 9x)) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0

Subproblem 2
Set the factor '(2y + 9x)' equal to zero and attempt to solve:

Simplifying
2y + 9x = 0

Reorder the terms:
9x + 2y = 0

Solving
9x + 2y = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2y' to each side of the equation.
9x + 2y + -2y = 0 + -2y

Combine like terms: 2y + -2y = 0
9x + 0 = 0 + -2y
9x = 0 + -2y
Remove the zero:
9x = -2y

Divide each side by '9'.
x = -0.2222222222y

Simplifying
x = -0.2222222222y

Subproblem 3
Set the factor '(-2y + 9x)' equal to zero and attempt to solve:

Simplifying
-2y + 9x = 0

Reorder the terms:
9x + -2y = 0

Solving
9x + -2y = 0

Move all terms containing x to the left, all other terms to the right.

Add '2y' to each side of the equation.
9x + -2y + 2y = 0 + 2y

Combine like terms: -2y + 2y = 0
9x + 0 = 0 + 2y
9x = 0 + 2y
Remove the zero:
9x = 2y

Divide each side by '9'.
x = 0.2222222222y

Simplifying
x = 0.2222222222y
Solution
x = {0, -0.2222222222y, 0.2222222222y}

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