((2x^2+3y^2-7)x)dx-((3x^2+2y^2-8)y)dy=0

Solution for ((2x^2+3y^2-7)x)dx-((3x^2+2y^2-8)y)dy=0 equation:

Simplifying
((2x2 + 3y2 + -7) * x) * dx + -1((3x2 + 2y2 + -8) * y) * dy = 0

Reorder the terms:
((-7 + 2x2 + 3y2) * x) * dx + -1((3x2 + 2y2 + -8) * y) * dy = 0

Reorder the terms for easier multiplication:
(x(-7 + 2x2 + 3y2)) * dx + -1((3x2 + 2y2 + -8) * y) * dy = 0
((-7 * x + 2x2 * x + 3y2 * x)) * dx + -1((3x2 + 2y2 + -8) * y) * dy = 0

Reorder the terms:
((-7x + 3xy2 + 2x3)) * dx + -1((3x2 + 2y2 + -8) * y) * dy = 0
((-7x + 3xy2 + 2x3)) * dx + -1((3x2 + 2y2 + -8) * y) * dy = 0

Reorder the terms for easier multiplication:
dx(-7x + 3xy2 + 2x3) + -1((3x2 + 2y2 + -8) * y) * dy = 0
(-7x * dx + 3xy2 * dx + 2x3 * dx) + -1((3x2 + 2y2 + -8) * y) * dy = 0
(-7dx2 + 3dx2y2 + 2dx4) + -1((3x2 + 2y2 + -8) * y) * dy = 0

Reorder the terms:
-7dx2 + 3dx2y2 + 2dx4 + -1((-8 + 3x2 + 2y2) * y) * dy = 0

Reorder the terms for easier multiplication:
-7dx2 + 3dx2y2 + 2dx4 + -1(y(-8 + 3x2 + 2y2)) * dy = 0
-7dx2 + 3dx2y2 + 2dx4 + -1((-8 * y + 3x2 * y + 2y2 * y)) * dy = 0

Reorder the terms:
-7dx2 + 3dx2y2 + 2dx4 + -1((3x2y + -8y + 2y3)) * dy = 0
-7dx2 + 3dx2y2 + 2dx4 + -1((3x2y + -8y + 2y3)) * dy = 0

Reorder the terms for easier multiplication:
-7dx2 + 3dx2y2 + 2dx4 + -1dy(3x2y + -8y + 2y3) = 0
-7dx2 + 3dx2y2 + 2dx4 + (3x2y * -1dy + -8y * -1dy + 2y3 * -1dy) = 0
-7dx2 + 3dx2y2 + 2dx4 + (-3dx2y2 + 8dy2 + -2dy4) = 0

Reorder the terms:
-7dx2 + 3dx2y2 + -3dx2y2 + 2dx4 + 8dy2 + -2dy4 = 0

Combine like terms: 3dx2y2 + -3dx2y2 = 0
-7dx2 + 0 + 2dx4 + 8dy2 + -2dy4 = 0
-7dx2 + 2dx4 + 8dy2 + -2dy4 = 0

Solving
-7dx2 + 2dx4 + 8dy2 + -2dy4 = 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(-7x2 + 2x4 + 8y2 + -2y4) = 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 '(-7x2 + 2x4 + 8y2 + -2y4)' equal to zero and attempt to solve:

Simplifying
-7x2 + 2x4 + 8y2 + -2y4 = 0

Solving
-7x2 + 2x4 + 8y2 + -2y4 = 0

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

Add '7x2' to each side of the equation.
-7x2 + 2x4 + 8y2 + 7x2 + -2y4 = 0 + 7x2

Reorder the terms:
-7x2 + 7x2 + 2x4 + 8y2 + -2y4 = 0 + 7x2

Combine like terms: -7x2 + 7x2 = 0
0 + 2x4 + 8y2 + -2y4 = 0 + 7x2
2x4 + 8y2 + -2y4 = 0 + 7x2
Remove the zero:
2x4 + 8y2 + -2y4 = 7x2

Add '-2x4' to each side of the equation.
2x4 + 8y2 + -2x4 + -2y4 = 7x2 + -2x4

Reorder the terms:
2x4 + -2x4 + 8y2 + -2y4 = 7x2 + -2x4

Combine like terms: 2x4 + -2x4 = 0
0 + 8y2 + -2y4 = 7x2 + -2x4
8y2 + -2y4 = 7x2 + -2x4

Add '-8y2' to each side of the equation.
8y2 + -8y2 + -2y4 = 7x2 + -2x4 + -8y2

Combine like terms: 8y2 + -8y2 = 0
0 + -2y4 = 7x2 + -2x4 + -8y2
-2y4 = 7x2 + -2x4 + -8y2

Add '2y4' to each side of the equation.
-2y4 + 2y4 = 7x2 + -2x4 + -8y2 + 2y4

Combine like terms: -2y4 + 2y4 = 0
0 = 7x2 + -2x4 + -8y2 + 2y4

Simplifying
0 = 7x2 + -2x4 + -8y2 + 2y4

The solution to this equation could not be determined.

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