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

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


Simplifying
((2x2) + -3)(dx) + ((2x2) * y + 4)(dy) = 0

Reorder the terms:
(-3 + (2x2))(dx) + ((2x2) * y + 4)(dy) = 0

Reorder the terms for easier multiplication:
dx(-3 + (2x2)) + ((2x2) * y + 4)(dy) = 0
(-3 * dx + (2x2) * dx) + ((2x2) * y + 4)(dy) = 0
(-3dx + 2dx3) + ((2x2) * y + 4)(dy) = 0

Remove parenthesis around (2x2)
-3dx + 2dx3 + (2x2 * y + 4)(dy) = 0

Multiply x2 * y
-3dx + 2dx3 + (2x2y + 4)(dy) = 0

Reorder the terms:
-3dx + 2dx3 + (4 + 2x2y)(dy) = 0

Reorder the terms for easier multiplication:
-3dx + 2dx3 + dy(4 + 2x2y) = 0
-3dx + 2dx3 + (4 * dy + 2x2y * dy) = 0

Reorder the terms:
-3dx + 2dx3 + (2dx2y2 + 4dy) = 0
-3dx + 2dx3 + (2dx2y2 + 4dy) = 0

Reorder the terms:
-3dx + 2dx2y2 + 2dx3 + 4dy = 0

Solving
-3dx + 2dx2y2 + 2dx3 + 4dy = 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(-3x + 2x2y2 + 2x3 + 4y) = 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 '(-3x + 2x2y2 + 2x3 + 4y)' equal to zero and attempt to solve:

Simplifying
-3x + 2x2y2 + 2x3 + 4y = 0

Solving
-3x + 2x2y2 + 2x3 + 4y = 0

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

Add '3x' to each side of the equation.
-3x + 2x2y2 + 2x3 + 3x + 4y = 0 + 3x

Reorder the terms:
-3x + 3x + 2x2y2 + 2x3 + 4y = 0 + 3x

Combine like terms: -3x + 3x = 0
0 + 2x2y2 + 2x3 + 4y = 0 + 3x
2x2y2 + 2x3 + 4y = 0 + 3x
Remove the zero:
2x2y2 + 2x3 + 4y = 3x

Add '-2x2y2' to each side of the equation.
2x2y2 + 2x3 + -2x2y2 + 4y = 3x + -2x2y2

Reorder the terms:
2x2y2 + -2x2y2 + 2x3 + 4y = 3x + -2x2y2

Combine like terms: 2x2y2 + -2x2y2 = 0
0 + 2x3 + 4y = 3x + -2x2y2
2x3 + 4y = 3x + -2x2y2

Add '-2x3' to each side of the equation.
2x3 + -2x3 + 4y = 3x + -2x2y2 + -2x3

Combine like terms: 2x3 + -2x3 = 0
0 + 4y = 3x + -2x2y2 + -2x3
4y = 3x + -2x2y2 + -2x3

Add '-4y' to each side of the equation.
4y + -4y = 3x + -2x2y2 + -2x3 + -4y

Combine like terms: 4y + -4y = 0
0 = 3x + -2x2y2 + -2x3 + -4y

Simplifying
0 = 3x + -2x2y2 + -2x3 + -4y

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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