x(2y-3)dx+(x^2+1)dy=0

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Solution for x(2y-3)dx+(x^2+1)dy=0 equation: 


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

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

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

Multiply x * dx
dx2(-3 + 2y) + (x2 + 1) * dy = 0
(-3 * dx2 + 2y * dx2) + (x2 + 1) * dy = 0
(-3dx2 + 2dx2y) + (x2 + 1) * dy = 0

Reorder the terms:
-3dx2 + 2dx2y + (1 + x2) * dy = 0

Reorder the terms for easier multiplication:
-3dx2 + 2dx2y + dy(1 + x2) = 0
-3dx2 + 2dx2y + (1 * dy + x2 * dy) = 0

Reorder the terms:
-3dx2 + 2dx2y + (dx2y + 1dy) = 0
-3dx2 + 2dx2y + (dx2y + 1dy) = 0

Combine like terms: 2dx2y + dx2y = 3dx2y
-3dx2 + 3dx2y + 1dy = 0

Solving
-3dx2 + 3dx2y + 1dy = 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(-3x2 + 3x2y + y) = 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 '(-3x2 + 3x2y + y)' equal to zero and attempt to solve:

Simplifying
-3x2 + 3x2y + y = 0

Solving
-3x2 + 3x2y + y = 0

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

Add '3x2' to each side of the equation.
-3x2 + 3x2y + 3x2 + y = 0 + 3x2

Reorder the terms:
-3x2 + 3x2 + 3x2y + y = 0 + 3x2

Combine like terms: -3x2 + 3x2 = 0
0 + 3x2y + y = 0 + 3x2
3x2y + y = 0 + 3x2
Remove the zero:
3x2y + y = 3x2

Add '-3x2y' to each side of the equation.
3x2y + -3x2y + y = 3x2 + -3x2y

Combine like terms: 3x2y + -3x2y = 0
0 + y = 3x2 + -3x2y
y = 3x2 + -3x2y

Add '-1y' to each side of the equation.
y + -1y = 3x2 + -3x2y + -1y

Combine like terms: y + -1y = 0
0 = 3x2 + -3x2y + -1y

Simplifying
0 = 3x2 + -3x2y + -1y

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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