2x^3y-12x^2y^2+10xy^3=0

Solution for 2x^3y-12x^2y^2+10xy^3=0 equation:

Simplifying
2x3y + -12x2y2 + 10xy3 = 0

Reorder the terms:
10xy3 + -12x2y2 + 2x3y = 0

Solving
10xy3 + -12x2y2 + 2x3y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2xy'.
2xy(5y2 + -6xy + x2) = 0

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

Ignore the factor 2.
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 '(y + -1x)' equal to zero and attempt to solve:

Simplifying
y + -1x = 0

Reorder the terms:
-1x + y = 0

Solving
-1x + y = 0

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

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

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

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

Simplifying
x = y
Subproblem 3
Set the factor '(5y + -1x)' equal to zero and attempt to solve:

Simplifying
5y + -1x = 0

Reorder the terms:
-1x + 5y = 0

Solving
-1x + 5y = 0

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

Add '-5y' to each side of the equation.
-1x + 5y + -5y = 0 + -5y

Combine like terms: 5y + -5y = 0
-1x + 0 = 0 + -5y
-1x = 0 + -5y
Remove the zero:
-1x = -5y

Divide each side by '-1'.
x = 5y

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