(3x+2y-4)dx+(5x-3y+25)dy=0

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Solution for (3x+2y-4)dx+(5x-3y+25)dy=0 equation: 


Simplifying
(3x + 2y + -4) * dx + (5x + -3y + 25) * dy = 0

Reorder the terms:
(-4 + 3x + 2y) * dx + (5x + -3y + 25) * dy = 0

Reorder the terms for easier multiplication:
dx(-4 + 3x + 2y) + (5x + -3y + 25) * dy = 0
(-4 * dx + 3x * dx + 2y * dx) + (5x + -3y + 25) * dy = 0

Reorder the terms:
(-4dx + 2dxy + 3dx2) + (5x + -3y + 25) * dy = 0
(-4dx + 2dxy + 3dx2) + (5x + -3y + 25) * dy = 0

Reorder the terms:
-4dx + 2dxy + 3dx2 + (25 + 5x + -3y) * dy = 0

Reorder the terms for easier multiplication:
-4dx + 2dxy + 3dx2 + dy(25 + 5x + -3y) = 0
-4dx + 2dxy + 3dx2 + (25 * dy + 5x * dy + -3y * dy) = 0

Reorder the terms:
-4dx + 2dxy + 3dx2 + (5dxy + 25dy + -3dy2) = 0
-4dx + 2dxy + 3dx2 + (5dxy + 25dy + -3dy2) = 0

Reorder the terms:
-4dx + 2dxy + 5dxy + 3dx2 + 25dy + -3dy2 = 0

Combine like terms: 2dxy + 5dxy = 7dxy
-4dx + 7dxy + 3dx2 + 25dy + -3dy2 = 0

Solving
-4dx + 7dxy + 3dx2 + 25dy + -3dy2 = 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(-4x + 7xy + 3x2 + 25y + -3y2) = 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 '(-4x + 7xy + 3x2 + 25y + -3y2)' equal to zero and attempt to solve:

Simplifying
-4x + 7xy + 3x2 + 25y + -3y2 = 0

Solving
-4x + 7xy + 3x2 + 25y + -3y2 = 0

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

Add '4x' to each side of the equation.
-4x + 7xy + 3x2 + 25y + 4x + -3y2 = 0 + 4x

Reorder the terms:
-4x + 4x + 7xy + 3x2 + 25y + -3y2 = 0 + 4x

Combine like terms: -4x + 4x = 0
0 + 7xy + 3x2 + 25y + -3y2 = 0 + 4x
7xy + 3x2 + 25y + -3y2 = 0 + 4x
Remove the zero:
7xy + 3x2 + 25y + -3y2 = 4x

Add '-7xy' to each side of the equation.
7xy + 3x2 + 25y + -7xy + -3y2 = 4x + -7xy

Reorder the terms:
7xy + -7xy + 3x2 + 25y + -3y2 = 4x + -7xy

Combine like terms: 7xy + -7xy = 0
0 + 3x2 + 25y + -3y2 = 4x + -7xy
3x2 + 25y + -3y2 = 4x + -7xy

Add '-3x2' to each side of the equation.
3x2 + 25y + -3x2 + -3y2 = 4x + -7xy + -3x2

Reorder the terms:
3x2 + -3x2 + 25y + -3y2 = 4x + -7xy + -3x2

Combine like terms: 3x2 + -3x2 = 0
0 + 25y + -3y2 = 4x + -7xy + -3x2
25y + -3y2 = 4x + -7xy + -3x2

Add '-25y' to each side of the equation.
25y + -25y + -3y2 = 4x + -7xy + -3x2 + -25y

Combine like terms: 25y + -25y = 0
0 + -3y2 = 4x + -7xy + -3x2 + -25y
-3y2 = 4x + -7xy + -3x2 + -25y

Add '3y2' to each side of the equation.
-3y2 + 3y2 = 4x + -7xy + -3x2 + -25y + 3y2

Combine like terms: -3y2 + 3y2 = 0
0 = 4x + -7xy + -3x2 + -25y + 3y2

Simplifying
0 = 4x + -7xy + -3x2 + -25y + 3y2

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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