(2x+3y-7)dx-(3x+2y-8)dy=0

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Solution for (2x+3y-7)dx-(3x+2y-8)dy=0 equation: 


Simplifying
(2x + 3y + -7) * dx + -1(3x + 2y + -8) * dy = 0

Reorder the terms:
(-7 + 2x + 3y) * dx + -1(3x + 2y + -8) * dy = 0

Reorder the terms for easier multiplication:
dx(-7 + 2x + 3y) + -1(3x + 2y + -8) * dy = 0
(-7 * dx + 2x * dx + 3y * dx) + -1(3x + 2y + -8) * dy = 0

Reorder the terms:
(-7dx + 3dxy + 2dx2) + -1(3x + 2y + -8) * dy = 0
(-7dx + 3dxy + 2dx2) + -1(3x + 2y + -8) * dy = 0

Reorder the terms:
-7dx + 3dxy + 2dx2 + -1(-8 + 3x + 2y) * dy = 0

Reorder the terms for easier multiplication:
-7dx + 3dxy + 2dx2 + -1dy(-8 + 3x + 2y) = 0
-7dx + 3dxy + 2dx2 + (-8 * -1dy + 3x * -1dy + 2y * -1dy) = 0

Reorder the terms:
-7dx + 3dxy + 2dx2 + (-3dxy + 8dy + -2dy2) = 0
-7dx + 3dxy + 2dx2 + (-3dxy + 8dy + -2dy2) = 0

Reorder the terms:
-7dx + 3dxy + -3dxy + 2dx2 + 8dy + -2dy2 = 0

Combine like terms: 3dxy + -3dxy = 0
-7dx + 0 + 2dx2 + 8dy + -2dy2 = 0
-7dx + 2dx2 + 8dy + -2dy2 = 0

Solving
-7dx + 2dx2 + 8dy + -2dy2 = 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(-7x + 2x2 + 8y + -2y2) = 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 '(-7x + 2x2 + 8y + -2y2)' equal to zero and attempt to solve:

Simplifying
-7x + 2x2 + 8y + -2y2 = 0

Solving
-7x + 2x2 + 8y + -2y2 = 0

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

Add '7x' to each side of the equation.
-7x + 2x2 + 8y + 7x + -2y2 = 0 + 7x

Reorder the terms:
-7x + 7x + 2x2 + 8y + -2y2 = 0 + 7x

Combine like terms: -7x + 7x = 0
0 + 2x2 + 8y + -2y2 = 0 + 7x
2x2 + 8y + -2y2 = 0 + 7x
Remove the zero:
2x2 + 8y + -2y2 = 7x

Add '-2x2' to each side of the equation.
2x2 + 8y + -2x2 + -2y2 = 7x + -2x2

Reorder the terms:
2x2 + -2x2 + 8y + -2y2 = 7x + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 + 8y + -2y2 = 7x + -2x2
8y + -2y2 = 7x + -2x2

Add '-8y' to each side of the equation.
8y + -8y + -2y2 = 7x + -2x2 + -8y

Combine like terms: 8y + -8y = 0
0 + -2y2 = 7x + -2x2 + -8y
-2y2 = 7x + -2x2 + -8y

Add '2y2' to each side of the equation.
-2y2 + 2y2 = 7x + -2x2 + -8y + 2y2

Combine like terms: -2y2 + 2y2 = 0
0 = 7x + -2x2 + -8y + 2y2

Simplifying
0 = 7x + -2x2 + -8y + 2y2

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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