5x^3y-25x^2y^2+30xy^3=0

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Solution for 5x^3y-25x^2y^2+30xy^3=0 equation: 


Simplifying
5x3y + -25x2y2 + 30xy3 = 0

Reorder the terms:
30xy3 + -25x2y2 + 5x3y = 0

Solving
30xy3 + -25x2y2 + 5x3y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5xy'.
5xy(6y2 + -5xy + x2) = 0

Factor a trinomial.
5xy((2y + -1x)(3y + -1x)) = 0

Ignore the factor 5.

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

Simplifying
xy = 0

Solving
xy = 0

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

Simplifying
xy = 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 '(2y + -1x)' equal to zero and attempt to solve:

Simplifying
2y + -1x = 0

Reorder the terms:
-1x + 2y = 0

Solving
-1x + 2y = 0

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

Add '-2y' to each side of the equation.
-1x + 2y + -2y = 0 + -2y

Combine like terms: 2y + -2y = 0
-1x + 0 = 0 + -2y
-1x = 0 + -2y
Remove the zero:
-1x = -2y

Divide each side by '-1'.
x = 2y

Simplifying
x = 2y

Subproblem 3
Set the factor '(3y + -1x)' equal to zero and attempt to solve:

Simplifying
3y + -1x = 0

Reorder the terms:
-1x + 3y = 0

Solving
-1x + 3y = 0

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

Add '-3y' to each side of the equation.
-1x + 3y + -3y = 0 + -3y

Combine like terms: 3y + -3y = 0
-1x + 0 = 0 + -3y
-1x = 0 + -3y
Remove the zero:
-1x = -3y

Divide each side by '-1'.
x = 3y

Simplifying
x = 3y
Solution
x = {2y, 3y}

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