(2x-y^2)dx+2(3y^2-xy)dy=0

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


Simplifying
(2x + -1y2) * dx + 2(3y2 + -1xy) * dy = 0

Reorder the terms for easier multiplication:
dx(2x + -1y2) + 2(3y2 + -1xy) * dy = 0
(2x * dx + -1y2 * dx) + 2(3y2 + -1xy) * dy = 0

Reorder the terms:
(-1dxy2 + 2dx2) + 2(3y2 + -1xy) * dy = 0
(-1dxy2 + 2dx2) + 2(3y2 + -1xy) * dy = 0

Reorder the terms:
-1dxy2 + 2dx2 + 2(-1xy + 3y2) * dy = 0

Reorder the terms for easier multiplication:
-1dxy2 + 2dx2 + 2dy(-1xy + 3y2) = 0
-1dxy2 + 2dx2 + (-1xy * 2dy + 3y2 * 2dy) = 0
-1dxy2 + 2dx2 + (-2dxy2 + 6dy3) = 0

Reorder the terms:
-1dxy2 + -2dxy2 + 2dx2 + 6dy3 = 0

Combine like terms: -1dxy2 + -2dxy2 = -3dxy2
-3dxy2 + 2dx2 + 6dy3 = 0

Solving
-3dxy2 + 2dx2 + 6dy3 = 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(-3xy2 + 2x2 + 6y3) = 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 '(-3xy2 + 2x2 + 6y3)' equal to zero and attempt to solve:

Simplifying
-3xy2 + 2x2 + 6y3 = 0

Solving
-3xy2 + 2x2 + 6y3 = 0

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

Add '3xy2' to each side of the equation.
-3xy2 + 2x2 + 3xy2 + 6y3 = 0 + 3xy2

Reorder the terms:
-3xy2 + 3xy2 + 2x2 + 6y3 = 0 + 3xy2

Combine like terms: -3xy2 + 3xy2 = 0
0 + 2x2 + 6y3 = 0 + 3xy2
2x2 + 6y3 = 0 + 3xy2
Remove the zero:
2x2 + 6y3 = 3xy2

Add '-2x2' to each side of the equation.
2x2 + -2x2 + 6y3 = 3xy2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 + 6y3 = 3xy2 + -2x2
6y3 = 3xy2 + -2x2

Add '-6y3' to each side of the equation.
6y3 + -6y3 = 3xy2 + -2x2 + -6y3

Combine like terms: 6y3 + -6y3 = 0
0 = 3xy2 + -2x2 + -6y3

Simplifying
0 = 3xy2 + -2x2 + -6y3

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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