(12x+5y-9)dx+(5x+2y-3)dy=0

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Solution for (12x+5y-9)dx+(5x+2y-3)dy=0 equation: 


Simplifying
(12x + 5y + -9) * dx + (5x + 2y + -3) * dy = 0

Reorder the terms:
(-9 + 12x + 5y) * dx + (5x + 2y + -3) * dy = 0

Reorder the terms for easier multiplication:
dx(-9 + 12x + 5y) + (5x + 2y + -3) * dy = 0
(-9 * dx + 12x * dx + 5y * dx) + (5x + 2y + -3) * dy = 0

Reorder the terms:
(-9dx + 5dxy + 12dx2) + (5x + 2y + -3) * dy = 0
(-9dx + 5dxy + 12dx2) + (5x + 2y + -3) * dy = 0

Reorder the terms:
-9dx + 5dxy + 12dx2 + (-3 + 5x + 2y) * dy = 0

Reorder the terms for easier multiplication:
-9dx + 5dxy + 12dx2 + dy(-3 + 5x + 2y) = 0
-9dx + 5dxy + 12dx2 + (-3 * dy + 5x * dy + 2y * dy) = 0

Reorder the terms:
-9dx + 5dxy + 12dx2 + (5dxy + -3dy + 2dy2) = 0
-9dx + 5dxy + 12dx2 + (5dxy + -3dy + 2dy2) = 0

Reorder the terms:
-9dx + 5dxy + 5dxy + 12dx2 + -3dy + 2dy2 = 0

Combine like terms: 5dxy + 5dxy = 10dxy
-9dx + 10dxy + 12dx2 + -3dy + 2dy2 = 0

Solving
-9dx + 10dxy + 12dx2 + -3dy + 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(-9x + 10xy + 12x2 + -3y + 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 '(-9x + 10xy + 12x2 + -3y + 2y2)' equal to zero and attempt to solve:

Simplifying
-9x + 10xy + 12x2 + -3y + 2y2 = 0

Solving
-9x + 10xy + 12x2 + -3y + 2y2 = 0

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

Add '9x' to each side of the equation.
-9x + 10xy + 12x2 + -3y + 9x + 2y2 = 0 + 9x

Reorder the terms:
-9x + 9x + 10xy + 12x2 + -3y + 2y2 = 0 + 9x

Combine like terms: -9x + 9x = 0
0 + 10xy + 12x2 + -3y + 2y2 = 0 + 9x
10xy + 12x2 + -3y + 2y2 = 0 + 9x
Remove the zero:
10xy + 12x2 + -3y + 2y2 = 9x

Add '-10xy' to each side of the equation.
10xy + 12x2 + -3y + -10xy + 2y2 = 9x + -10xy

Reorder the terms:
10xy + -10xy + 12x2 + -3y + 2y2 = 9x + -10xy

Combine like terms: 10xy + -10xy = 0
0 + 12x2 + -3y + 2y2 = 9x + -10xy
12x2 + -3y + 2y2 = 9x + -10xy

Add '-12x2' to each side of the equation.
12x2 + -3y + -12x2 + 2y2 = 9x + -10xy + -12x2

Reorder the terms:
12x2 + -12x2 + -3y + 2y2 = 9x + -10xy + -12x2

Combine like terms: 12x2 + -12x2 = 0
0 + -3y + 2y2 = 9x + -10xy + -12x2
-3y + 2y2 = 9x + -10xy + -12x2

Add '3y' to each side of the equation.
-3y + 3y + 2y2 = 9x + -10xy + -12x2 + 3y

Combine like terms: -3y + 3y = 0
0 + 2y2 = 9x + -10xy + -12x2 + 3y
2y2 = 9x + -10xy + -12x2 + 3y

Add '-2y2' to each side of the equation.
2y2 + -2y2 = 9x + -10xy + -12x2 + 3y + -2y2

Combine like terms: 2y2 + -2y2 = 0
0 = 9x + -10xy + -12x2 + 3y + -2y2

Simplifying
0 = 9x + -10xy + -12x2 + 3y + -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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