-27x^5+75x^3y^2=0

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Solution for -27x^5+75x^3y^2=0 equation: 


Simplifying
-27x5 + 75x3y2 = 0

Reorder the terms:
75x3y2 + -27x5 = 0

Solving
75x3y2 + -27x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x3'.
3x3(25y2 + -9x2) = 0

Factor a difference between two squares.
3x3((5y + 3x)(5y + -3x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve:

Simplifying
x3 = 0

Solving
x3 = 0

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

Simplifying
x3 = 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 '(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 = {-1.666666667y, 1.666666667y}

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