4x^4y-12x^3y^2-40x^2y^3=0

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Solution for 4x^4y-12x^3y^2-40x^2y^3=0 equation: 


Simplifying
4x4y + -12x3y2 + -40x2y3 = 0

Reorder the terms:
-40x2y3 + -12x3y2 + 4x4y = 0

Solving
-40x2y3 + -12x3y2 + 4x4y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x2y'.
4x2y(-10y2 + -3xy + x2) = 0

Factor a trinomial.
4x2y((-2y + -1x)(5y + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor 'x2y' equal to zero and attempt to solve:

Simplifying
x2y = 0

Solving
x2y = 0

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

Simplifying
x2y = 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 '(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 = {-2y, 5y}

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