27x^3-75xy^2=0

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Solution for 27x^3-75xy^2=0 equation: 


Simplifying
27x3 + -75xy2 = 0

Reorder the terms:
-75xy2 + 27x3 = 0

Solving
-75xy2 + 27x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-25y2 + 9x2) = 0

Factor a difference between two squares.
3x((5y + 3x)(-5y + 3x)) = 0

Ignore the factor 3.

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 '(5y + 3x)' equal to zero and attempt to solve:

Simplifying
5y + 3x = 0

Reorder the terms:
3x + 5y = 0

Solving
3x + 5y = 0

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

Add '-5y' to each side of the equation.
3x + 5y + -5y = 0 + -5y

Combine like terms: 5y + -5y = 0
3x + 0 = 0 + -5y
3x = 0 + -5y
Remove the zero:
3x = -5y

Divide each side by '3'.
x = -1.666666667y

Simplifying
x = -1.666666667y

Subproblem 3
Set the factor '(-5y + 3x)' equal to zero and attempt to solve:

Simplifying
-5y + 3x = 0

Reorder the terms:
3x + -5y = 0

Solving
3x + -5y = 0

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

Add '5y' to each side of the equation.
3x + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
3x + 0 = 0 + 5y
3x = 0 + 5y
Remove the zero:
3x = 5y

Divide each side by '3'.
x = 1.666666667y

Simplifying
x = 1.666666667y
Solution
x = {0, -1.666666667y, 1.666666667y}

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