(4x+3y+15)dx+(2x+y+7)dy=0

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Solution for (4x+3y+15)dx+(2x+y+7)dy=0 equation: 


Simplifying
(4x + 3y + 15) * dx + (2x + y + 7) * dy = 0

Reorder the terms:
(15 + 4x + 3y) * dx + (2x + y + 7) * dy = 0

Reorder the terms for easier multiplication:
dx(15 + 4x + 3y) + (2x + y + 7) * dy = 0
(15 * dx + 4x * dx + 3y * dx) + (2x + y + 7) * dy = 0

Reorder the terms:
(15dx + 3dxy + 4dx2) + (2x + y + 7) * dy = 0
(15dx + 3dxy + 4dx2) + (2x + y + 7) * dy = 0

Reorder the terms:
15dx + 3dxy + 4dx2 + (7 + 2x + y) * dy = 0

Reorder the terms for easier multiplication:
15dx + 3dxy + 4dx2 + dy(7 + 2x + y) = 0
15dx + 3dxy + 4dx2 + (7 * dy + 2x * dy + y * dy) = 0

Reorder the terms:
15dx + 3dxy + 4dx2 + (2dxy + 7dy + dy2) = 0
15dx + 3dxy + 4dx2 + (2dxy + 7dy + dy2) = 0

Reorder the terms:
15dx + 3dxy + 2dxy + 4dx2 + 7dy + dy2 = 0

Combine like terms: 3dxy + 2dxy = 5dxy
15dx + 5dxy + 4dx2 + 7dy + dy2 = 0

Solving
15dx + 5dxy + 4dx2 + 7dy + dy2 = 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(15x + 5xy + 4x2 + 7y + y2) = 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 '(15x + 5xy + 4x2 + 7y + y2)' equal to zero and attempt to solve:

Simplifying
15x + 5xy + 4x2 + 7y + y2 = 0

Solving
15x + 5xy + 4x2 + 7y + y2 = 0

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

Add '-15x' to each side of the equation.
15x + 5xy + 4x2 + 7y + -15x + y2 = 0 + -15x

Reorder the terms:
15x + -15x + 5xy + 4x2 + 7y + y2 = 0 + -15x

Combine like terms: 15x + -15x = 0
0 + 5xy + 4x2 + 7y + y2 = 0 + -15x
5xy + 4x2 + 7y + y2 = 0 + -15x
Remove the zero:
5xy + 4x2 + 7y + y2 = -15x

Add '-5xy' to each side of the equation.
5xy + 4x2 + 7y + -5xy + y2 = -15x + -5xy

Reorder the terms:
5xy + -5xy + 4x2 + 7y + y2 = -15x + -5xy

Combine like terms: 5xy + -5xy = 0
0 + 4x2 + 7y + y2 = -15x + -5xy
4x2 + 7y + y2 = -15x + -5xy

Add '-4x2' to each side of the equation.
4x2 + 7y + -4x2 + y2 = -15x + -5xy + -4x2

Reorder the terms:
4x2 + -4x2 + 7y + y2 = -15x + -5xy + -4x2

Combine like terms: 4x2 + -4x2 = 0
0 + 7y + y2 = -15x + -5xy + -4x2
7y + y2 = -15x + -5xy + -4x2

Add '-7y' to each side of the equation.
7y + -7y + y2 = -15x + -5xy + -4x2 + -7y

Combine like terms: 7y + -7y = 0
0 + y2 = -15x + -5xy + -4x2 + -7y
y2 = -15x + -5xy + -4x2 + -7y

Add '-1y2' to each side of the equation.
y2 + -1y2 = -15x + -5xy + -4x2 + -7y + -1y2

Combine like terms: y2 + -1y2 = 0
0 = -15x + -5xy + -4x2 + -7y + -1y2

Simplifying
0 = -15x + -5xy + -4x2 + -7y + -1y2

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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