(2-9xy^2)x*dx+(4y^2-6x^3)y*dy=0

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Solution for (2-9xy^2)x*dx+(4y^2-6x^3)y*dy=0 equation: 


Simplifying
(2 + -9xy2) * x * dx + (4y2 + -6x3) * y * dy = 0

Reorder the terms for easier multiplication:
x * dx(2 + -9xy2) + (4y2 + -6x3) * y * dy = 0

Multiply x * dx
dx2(2 + -9xy2) + (4y2 + -6x3) * y * dy = 0
(2 * dx2 + -9xy2 * dx2) + (4y2 + -6x3) * y * dy = 0
(2dx2 + -9dx3y2) + (4y2 + -6x3) * y * dy = 0

Reorder the terms:
2dx2 + -9dx3y2 + (-6x3 + 4y2) * y * dy = 0

Reorder the terms for easier multiplication:
2dx2 + -9dx3y2 + y * dy(-6x3 + 4y2) = 0

Multiply y * dy
2dx2 + -9dx3y2 + dy2(-6x3 + 4y2) = 0
2dx2 + -9dx3y2 + (-6x3 * dy2 + 4y2 * dy2) = 0
2dx2 + -9dx3y2 + (-6dx3y2 + 4dy4) = 0

Combine like terms: -9dx3y2 + -6dx3y2 = -15dx3y2
2dx2 + -15dx3y2 + 4dy4 = 0

Solving
2dx2 + -15dx3y2 + 4dy4 = 0

Solving for variable 'd'.

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

Factor out the Greatest Common Factor (GCF), 'd'.
d(2x2 + -15x3y2 + 4y4) = 0


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

Simplifying
d = 0

Solving
d = 0

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

Simplifying
d = 0

Subproblem 2
Set the factor '(2x2 + -15x3y2 + 4y4)' equal to zero and attempt to solve:

Simplifying
2x2 + -15x3y2 + 4y4 = 0

Solving
2x2 + -15x3y2 + 4y4 = 0

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

Add '-2x2' to each side of the equation.
2x2 + -15x3y2 + -2x2 + 4y4 = 0 + -2x2

Reorder the terms:
2x2 + -2x2 + -15x3y2 + 4y4 = 0 + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 + -15x3y2 + 4y4 = 0 + -2x2
-15x3y2 + 4y4 = 0 + -2x2
Remove the zero:
-15x3y2 + 4y4 = -2x2

Add '15x3y2' to each side of the equation.
-15x3y2 + 15x3y2 + 4y4 = -2x2 + 15x3y2

Combine like terms: -15x3y2 + 15x3y2 = 0
0 + 4y4 = -2x2 + 15x3y2
4y4 = -2x2 + 15x3y2

Add '-4y4' to each side of the equation.
4y4 + -4y4 = -2x2 + 15x3y2 + -4y4

Combine like terms: 4y4 + -4y4 = 0
0 = -2x2 + 15x3y2 + -4y4

Simplifying
0 = -2x2 + 15x3y2 + -4y4

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
d = {0}

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