(9x-4y+4)dx-(2x-y-1)dy=0

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Solution for (9x-4y+4)dx-(2x-y-1)dy=0 equation: 


Simplifying
(9x + -4y + 4) * dx + -1(2x + -1y + -1) * dy = 0

Reorder the terms:
(4 + 9x + -4y) * dx + -1(2x + -1y + -1) * dy = 0

Reorder the terms for easier multiplication:
dx(4 + 9x + -4y) + -1(2x + -1y + -1) * dy = 0
(4 * dx + 9x * dx + -4y * dx) + -1(2x + -1y + -1) * dy = 0

Reorder the terms:
(4dx + -4dxy + 9dx2) + -1(2x + -1y + -1) * dy = 0
(4dx + -4dxy + 9dx2) + -1(2x + -1y + -1) * dy = 0

Reorder the terms:
4dx + -4dxy + 9dx2 + -1(-1 + 2x + -1y) * dy = 0

Reorder the terms for easier multiplication:
4dx + -4dxy + 9dx2 + -1dy(-1 + 2x + -1y) = 0
4dx + -4dxy + 9dx2 + (-1 * -1dy + 2x * -1dy + -1y * -1dy) = 0

Reorder the terms:
4dx + -4dxy + 9dx2 + (-2dxy + 1dy + 1dy2) = 0
4dx + -4dxy + 9dx2 + (-2dxy + 1dy + 1dy2) = 0

Reorder the terms:
4dx + -4dxy + -2dxy + 9dx2 + 1dy + 1dy2 = 0

Combine like terms: -4dxy + -2dxy = -6dxy
4dx + -6dxy + 9dx2 + 1dy + 1dy2 = 0

Solving
4dx + -6dxy + 9dx2 + 1dy + 1dy2 = 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 + -6xy + 9x2 + y + 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 '(4x + -6xy + 9x2 + y + y2)' equal to zero and attempt to solve:

Simplifying
4x + -6xy + 9x2 + y + y2 = 0

Solving
4x + -6xy + 9x2 + y + y2 = 0

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

Add '-4x' to each side of the equation.
4x + -6xy + 9x2 + y + -4x + y2 = 0 + -4x

Reorder the terms:
4x + -4x + -6xy + 9x2 + y + y2 = 0 + -4x

Combine like terms: 4x + -4x = 0
0 + -6xy + 9x2 + y + y2 = 0 + -4x
-6xy + 9x2 + y + y2 = 0 + -4x
Remove the zero:
-6xy + 9x2 + y + y2 = -4x

Add '6xy' to each side of the equation.
-6xy + 9x2 + y + 6xy + y2 = -4x + 6xy

Reorder the terms:
-6xy + 6xy + 9x2 + y + y2 = -4x + 6xy

Combine like terms: -6xy + 6xy = 0
0 + 9x2 + y + y2 = -4x + 6xy
9x2 + y + y2 = -4x + 6xy

Add '-9x2' to each side of the equation.
9x2 + y + -9x2 + y2 = -4x + 6xy + -9x2

Reorder the terms:
9x2 + -9x2 + y + y2 = -4x + 6xy + -9x2

Combine like terms: 9x2 + -9x2 = 0
0 + y + y2 = -4x + 6xy + -9x2
y + y2 = -4x + 6xy + -9x2

Add '-1y' to each side of the equation.
y + -1y + y2 = -4x + 6xy + -9x2 + -1y

Combine like terms: y + -1y = 0
0 + y2 = -4x + 6xy + -9x2 + -1y
y2 = -4x + 6xy + -9x2 + -1y

Add '-1y2' to each side of the equation.
y2 + -1y2 = -4x + 6xy + -9x2 + -1y + -1y2

Combine like terms: y2 + -1y2 = 0
0 = -4x + 6xy + -9x2 + -1y + -1y2

Simplifying
0 = -4x + 6xy + -9x2 + -1y + -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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