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

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

Simplifying
y2 + -4xy3 + 4x2y4 = 0

Reorder the terms:
-4xy3 + 4x2y4 + y2 = 0

Solving
-4xy3 + 4x2y4 + y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'y2'.
y2(-4xy + 4x2y2 + 1) = 0

Factor a trinomial.
y2((2xy + -1)(2xy + -1)) = 0

Subproblem 1
Set the factor 'y2' equal to zero and attempt to solve:

Simplifying
y2 = 0

Solving
y2 = 0

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

Add '-1y2' to each side of the equation.
y2 + -1y2 = 0 + -1y2
Remove the zero:
0 = -1y2

Simplifying
0 = -1y2

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 '(2xy + -1)' equal to zero and attempt to solve:

Simplifying
2xy + -1 = 0

Reorder the terms:
-1 + 2xy = 0

Solving
-1 + 2xy = 0

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

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

Combine like terms: -1 + 1 = 0
0 + 2xy = 0 + 1
2xy = 0 + 1

Combine like terms: 0 + 1 = 1
2xy = 1

Divide each side by '2y'.
x = 0.5y-1

Simplifying
x = 0.5y-1
Subproblem 3
Set the factor '(2xy + -1)' equal to zero and attempt to solve:

Simplifying
2xy + -1 = 0

Reorder the terms:
-1 + 2xy = 0

Solving
-1 + 2xy = 0

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

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

Combine like terms: -1 + 1 = 0
0 + 2xy = 0 + 1
2xy = 0 + 1

Combine like terms: 0 + 1 = 1
2xy = 1

Divide each side by '2y'.
x = 0.5y-1

Simplifying
x = 0.5y-1
Solution
x = {0.5y-1, 0.5y-1}