2x^2y-6xy^2-80y^3=0

Solution for 2x^2y-6xy^2-80y^3=0 equation:

Simplifying
2x2y + -6xy2 + -80y3 = 0

Reorder the terms:
-6xy2 + 2x2y + -80y3 = 0

Solving
-6xy2 + 2x2y + -80y3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2y'.
2y(-3xy + x2 + -40y2) = 0

Factor a trinomial.
2y((x + -8y)(x + 5y)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

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

Simplifying
0 = -1y

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 '(x + -8y)' equal to zero and attempt to solve:

Simplifying
x + -8y = 0

Solving
x + -8y = 0

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

Add '8y' to each side of the equation.
x + -8y + 8y = 0 + 8y

Combine like terms: -8y + 8y = 0
x + 0 = 0 + 8y
x = 0 + 8y
Remove the zero:
x = 8y

Simplifying
x = 8y
Subproblem 3
Set the factor '(x + 5y)' equal to zero and attempt to solve:

Simplifying
x + 5y = 0

Solving
x + 5y = 0

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

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

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

Simplifying
x = -5y
Solution
x = {8y, -5y}