(x-4y-3)dx-(x-6y-5)y=0

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Solution for (x-4y-3)dx-(x-6y-5)y=0 equation: 


Simplifying
(x + -4y + -3) * dx + -1(x + -6y + -5) * y = 0

Reorder the terms:
(-3 + x + -4y) * dx + -1(x + -6y + -5) * y = 0

Reorder the terms for easier multiplication:
dx(-3 + x + -4y) + -1(x + -6y + -5) * y = 0
(-3 * dx + x * dx + -4y * dx) + -1(x + -6y + -5) * y = 0

Reorder the terms:
(-3dx + -4dxy + dx2) + -1(x + -6y + -5) * y = 0
(-3dx + -4dxy + dx2) + -1(x + -6y + -5) * y = 0

Reorder the terms:
-3dx + -4dxy + dx2 + -1(-5 + x + -6y) * y = 0

Reorder the terms for easier multiplication:
-3dx + -4dxy + dx2 + -1y(-5 + x + -6y) = 0
-3dx + -4dxy + dx2 + (-5 * -1y + x * -1y + -6y * -1y) = 0

Reorder the terms:
-3dx + -4dxy + dx2 + (-1xy + 5y + 6y2) = 0
-3dx + -4dxy + dx2 + (-1xy + 5y + 6y2) = 0

Solving
-3dx + -4dxy + dx2 + -1xy + 5y + 6y2 = 0

Solving for variable 'd'.

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

Add 'xy' to each side of the equation.
-3dx + -4dxy + dx2 + -1xy + 5y + xy + 6y2 = 0 + xy

Reorder the terms:
-3dx + -4dxy + dx2 + -1xy + xy + 5y + 6y2 = 0 + xy

Combine like terms: -1xy + xy = 0
-3dx + -4dxy + dx2 + 0 + 5y + 6y2 = 0 + xy
-3dx + -4dxy + dx2 + 5y + 6y2 = 0 + xy
Remove the zero:
-3dx + -4dxy + dx2 + 5y + 6y2 = xy

Add '-5y' to each side of the equation.
-3dx + -4dxy + dx2 + 5y + -5y + 6y2 = xy + -5y

Combine like terms: 5y + -5y = 0
-3dx + -4dxy + dx2 + 0 + 6y2 = xy + -5y
-3dx + -4dxy + dx2 + 6y2 = xy + -5y

Add '-6y2' to each side of the equation.
-3dx + -4dxy + dx2 + 6y2 + -6y2 = xy + -5y + -6y2

Combine like terms: 6y2 + -6y2 = 0
-3dx + -4dxy + dx2 + 0 = xy + -5y + -6y2
-3dx + -4dxy + dx2 = xy + -5y + -6y2

Reorder the terms:
-3dx + -4dxy + dx2 + -1xy + 5y + 6y2 = xy + -1xy + -5y + 5y + -6y2 + 6y2

Combine like terms: xy + -1xy = 0
-3dx + -4dxy + dx2 + -1xy + 5y + 6y2 = 0 + -5y + 5y + -6y2 + 6y2
-3dx + -4dxy + dx2 + -1xy + 5y + 6y2 = -5y + 5y + -6y2 + 6y2

Combine like terms: -5y + 5y = 0
-3dx + -4dxy + dx2 + -1xy + 5y + 6y2 = 0 + -6y2 + 6y2
-3dx + -4dxy + dx2 + -1xy + 5y + 6y2 = -6y2 + 6y2

Combine like terms: -6y2 + 6y2 = 0
-3dx + -4dxy + dx2 + -1xy + 5y + 6y2 = 0

The solution to this equation could not be determined.

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