(3x+2y-3)dx+(6x+4y)dy=0

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


Simplifying
(3x + 2y + -3) * dx + (6x + 4y) * dy = 0

Reorder the terms:
(-3 + 3x + 2y) * dx + (6x + 4y) * dy = 0

Reorder the terms for easier multiplication:
dx(-3 + 3x + 2y) + (6x + 4y) * dy = 0
(-3 * dx + 3x * dx + 2y * dx) + (6x + 4y) * dy = 0

Reorder the terms:
(-3dx + 2dxy + 3dx2) + (6x + 4y) * dy = 0
(-3dx + 2dxy + 3dx2) + (6x + 4y) * dy = 0

Reorder the terms for easier multiplication:
-3dx + 2dxy + 3dx2 + dy(6x + 4y) = 0
-3dx + 2dxy + 3dx2 + (6x * dy + 4y * dy) = 0
-3dx + 2dxy + 3dx2 + (6dxy + 4dy2) = 0

Reorder the terms:
-3dx + 2dxy + 6dxy + 3dx2 + 4dy2 = 0

Combine like terms: 2dxy + 6dxy = 8dxy
-3dx + 8dxy + 3dx2 + 4dy2 = 0

Solving
-3dx + 8dxy + 3dx2 + 4dy2 = 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 + 8xy + 3x2 + 4y2) = 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 + 8xy + 3x2 + 4y2)' equal to zero and attempt to solve:

Simplifying
-3x + 8xy + 3x2 + 4y2 = 0

Solving
-3x + 8xy + 3x2 + 4y2 = 0

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

Add '3x' to each side of the equation.
-3x + 8xy + 3x2 + 3x + 4y2 = 0 + 3x

Reorder the terms:
-3x + 3x + 8xy + 3x2 + 4y2 = 0 + 3x

Combine like terms: -3x + 3x = 0
0 + 8xy + 3x2 + 4y2 = 0 + 3x
8xy + 3x2 + 4y2 = 0 + 3x
Remove the zero:
8xy + 3x2 + 4y2 = 3x

Add '-8xy' to each side of the equation.
8xy + 3x2 + -8xy + 4y2 = 3x + -8xy

Reorder the terms:
8xy + -8xy + 3x2 + 4y2 = 3x + -8xy

Combine like terms: 8xy + -8xy = 0
0 + 3x2 + 4y2 = 3x + -8xy
3x2 + 4y2 = 3x + -8xy

Add '-3x2' to each side of the equation.
3x2 + -3x2 + 4y2 = 3x + -8xy + -3x2

Combine like terms: 3x2 + -3x2 = 0
0 + 4y2 = 3x + -8xy + -3x2
4y2 = 3x + -8xy + -3x2

Add '-4y2' to each side of the equation.
4y2 + -4y2 = 3x + -8xy + -3x2 + -4y2

Combine like terms: 4y2 + -4y2 = 0
0 = 3x + -8xy + -3x2 + -4y2

Simplifying
0 = 3x + -8xy + -3x2 + -4y2

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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