40x^4y^2+76x^3y^3-60x^2y^4=0

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Solution for 40x^4y^2+76x^3y^3-60x^2y^4=0 equation: 


Simplifying
40x4y2 + 76x3y3 + -60x2y4 = 0

Reorder the terms:
-60x2y4 + 76x3y3 + 40x4y2 = 0

Solving
-60x2y4 + 76x3y3 + 40x4y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x2y2'.
4x2y2(-15y2 + 19xy + 10x2) = 0

Factor a trinomial.
4x2y2((-5y + -2x)(3y + -5x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor 'x2y2' equal to zero and attempt to solve:

Simplifying
x2y2 = 0

Solving
x2y2 = 0

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

Simplifying
x2y2 = 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 '(-5y + -2x)' equal to zero and attempt to solve:

Simplifying
-5y + -2x = 0

Reorder the terms:
-2x + -5y = 0

Solving
-2x + -5y = 0

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

Add '5y' to each side of the equation.
-2x + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
-2x + 0 = 0 + 5y
-2x = 0 + 5y
Remove the zero:
-2x = 5y

Divide each side by '-2'.
x = -2.5y

Simplifying
x = -2.5y

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

Simplifying
3y + -5x = 0

Reorder the terms:
-5x + 3y = 0

Solving
-5x + 3y = 0

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

Add '-3y' to each side of the equation.
-5x + 3y + -3y = 0 + -3y

Combine like terms: 3y + -3y = 0
-5x + 0 = 0 + -3y
-5x = 0 + -3y
Remove the zero:
-5x = -3y

Divide each side by '-5'.
x = 0.6y

Simplifying
x = 0.6y
Solution
x = {-2.5y, 0.6y}

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