16x^3y+24x^2y^2-16xy^3=0

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Solution for 16x^3y+24x^2y^2-16xy^3=0 equation: 


Simplifying
16x3y + 24x2y2 + -16xy3 = 0

Reorder the terms:
-16xy3 + 24x2y2 + 16x3y = 0

Solving
-16xy3 + 24x2y2 + 16x3y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8xy'.
8xy(-2y2 + 3xy + 2x2) = 0

Factor a trinomial.
8xy((-2y + -1x)(y + -2x)) = 0

Ignore the factor 8.

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 '(y + -2x)' equal to zero and attempt to solve:

Simplifying
y + -2x = 0

Reorder the terms:
-2x + y = 0

Solving
-2x + y = 0

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

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

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

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

Simplifying
x = 0.5y
Solution
x = {-2y, 0.5y}

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