-5x^3y^2+20x^2y^3-20xy^4=0

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Solution for -5x^3y^2+20x^2y^3-20xy^4=0 equation: 


Simplifying
-5x3y2 + 20x2y3 + -20xy4 = 0

Reorder the terms:
-20xy4 + 20x2y3 + -5x3y2 = 0

Solving
-20xy4 + 20x2y3 + -5x3y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5xy2'.
5xy2(-4y2 + 4xy + -1x2) = 0

Factor a trinomial.
5xy2((-2y + x)(2y + -1x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor 'xy2' equal to zero and attempt to solve:

Simplifying
xy2 = 0

Solving
xy2 = 0

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

Simplifying
xy2 = 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 + x)' equal to zero and attempt to solve:

Simplifying
-2y + x = 0

Reorder the terms:
x + -2y = 0

Solving
x + -2y = 0

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

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

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

Simplifying
x = 2y

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

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