(10x*y-8y-3)dx+(5x^2-8x+6)dy=0

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Solution for (10x*y-8y-3)dx+(5x^2-8x+6)dy=0 equation: 


Simplifying
(10x * y + -8y + -3) * dx + (5x2 + -8x + 6) * dy = 0

Multiply x * y
(10xy + -8y + -3) * dx + (5x2 + -8x + 6) * dy = 0

Reorder the terms:
(-3 + 10xy + -8y) * dx + (5x2 + -8x + 6) * dy = 0

Reorder the terms for easier multiplication:
dx(-3 + 10xy + -8y) + (5x2 + -8x + 6) * dy = 0
(-3 * dx + 10xy * dx + -8y * dx) + (5x2 + -8x + 6) * dy = 0

Reorder the terms:
(-3dx + -8dxy + 10dx2y) + (5x2 + -8x + 6) * dy = 0
(-3dx + -8dxy + 10dx2y) + (5x2 + -8x + 6) * dy = 0

Reorder the terms:
-3dx + -8dxy + 10dx2y + (6 + -8x + 5x2) * dy = 0

Reorder the terms for easier multiplication:
-3dx + -8dxy + 10dx2y + dy(6 + -8x + 5x2) = 0
-3dx + -8dxy + 10dx2y + (6 * dy + -8x * dy + 5x2 * dy) = 0

Reorder the terms:
-3dx + -8dxy + 10dx2y + (-8dxy + 5dx2y + 6dy) = 0
-3dx + -8dxy + 10dx2y + (-8dxy + 5dx2y + 6dy) = 0

Reorder the terms:
-3dx + -8dxy + -8dxy + 10dx2y + 5dx2y + 6dy = 0

Combine like terms: -8dxy + -8dxy = -16dxy
-3dx + -16dxy + 10dx2y + 5dx2y + 6dy = 0

Combine like terms: 10dx2y + 5dx2y = 15dx2y
-3dx + -16dxy + 15dx2y + 6dy = 0

Solving
-3dx + -16dxy + 15dx2y + 6dy = 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 + -16xy + 15x2y + 6y) = 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 + -16xy + 15x2y + 6y)' equal to zero and attempt to solve:

Simplifying
-3x + -16xy + 15x2y + 6y = 0

Solving
-3x + -16xy + 15x2y + 6y = 0

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

Add '3x' to each side of the equation.
-3x + -16xy + 15x2y + 3x + 6y = 0 + 3x

Reorder the terms:
-3x + 3x + -16xy + 15x2y + 6y = 0 + 3x

Combine like terms: -3x + 3x = 0
0 + -16xy + 15x2y + 6y = 0 + 3x
-16xy + 15x2y + 6y = 0 + 3x
Remove the zero:
-16xy + 15x2y + 6y = 3x

Add '16xy' to each side of the equation.
-16xy + 15x2y + 16xy + 6y = 3x + 16xy

Reorder the terms:
-16xy + 16xy + 15x2y + 6y = 3x + 16xy

Combine like terms: -16xy + 16xy = 0
0 + 15x2y + 6y = 3x + 16xy
15x2y + 6y = 3x + 16xy

Add '-15x2y' to each side of the equation.
15x2y + -15x2y + 6y = 3x + 16xy + -15x2y

Combine like terms: 15x2y + -15x2y = 0
0 + 6y = 3x + 16xy + -15x2y
6y = 3x + 16xy + -15x2y

Add '-6y' to each side of the equation.
6y + -6y = 3x + 16xy + -15x2y + -6y

Combine like terms: 6y + -6y = 0
0 = 3x + 16xy + -15x2y + -6y

Simplifying
0 = 3x + 16xy + -15x2y + -6y

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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