(4Y+2X-1)dx+(6y+4x-5)dy=0

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Solution for (4Y+2X-1)dx+(6y+4x-5)dy=0 equation: 


Simplifying
(4Y + 2X + -1) * dx + (6y + 4x + -5) * dy = 0

Reorder the terms:
(-1 + 2X + 4Y) * dx + (6y + 4x + -5) * dy = 0

Reorder the terms for easier multiplication:
dx(-1 + 2X + 4Y) + (6y + 4x + -5) * dy = 0
(-1 * dx + 2X * dx + 4Y * dx) + (6y + 4x + -5) * dy = 0
(-1dx + 2dxX + 4dxY) + (6y + 4x + -5) * dy = 0

Reorder the terms:
-1dx + 2dxX + 4dxY + (-5 + 4x + 6y) * dy = 0

Reorder the terms for easier multiplication:
-1dx + 2dxX + 4dxY + dy(-5 + 4x + 6y) = 0
-1dx + 2dxX + 4dxY + (-5 * dy + 4x * dy + 6y * dy) = 0

Reorder the terms:
-1dx + 2dxX + 4dxY + (4dxy + -5dy + 6dy2) = 0
-1dx + 2dxX + 4dxY + (4dxy + -5dy + 6dy2) = 0

Solving
-1dx + 2dxX + 4dxY + 4dxy + -5dy + 6dy2 = 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(-1x + 2xX + 4xY + 4xy + -5y + 6y2) = 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 '(-1x + 2xX + 4xY + 4xy + -5y + 6y2)' equal to zero and attempt to solve:

Simplifying
-1x + 2xX + 4xY + 4xy + -5y + 6y2 = 0

Solving
-1x + 2xX + 4xY + 4xy + -5y + 6y2 = 0

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

Add 'x' to each side of the equation.
-1x + 2xX + 4xY + 4xy + -5y + x + 6y2 = 0 + x

Reorder the terms:
-1x + x + 2xX + 4xY + 4xy + -5y + 6y2 = 0 + x

Combine like terms: -1x + x = 0
0 + 2xX + 4xY + 4xy + -5y + 6y2 = 0 + x
2xX + 4xY + 4xy + -5y + 6y2 = 0 + x
Remove the zero:
2xX + 4xY + 4xy + -5y + 6y2 = x

Add '-2xX' to each side of the equation.
2xX + 4xY + 4xy + -5y + -2xX + 6y2 = x + -2xX

Reorder the terms:
2xX + -2xX + 4xY + 4xy + -5y + 6y2 = x + -2xX

Combine like terms: 2xX + -2xX = 0
0 + 4xY + 4xy + -5y + 6y2 = x + -2xX
4xY + 4xy + -5y + 6y2 = x + -2xX

Add '-4xY' to each side of the equation.
4xY + 4xy + -5y + -4xY + 6y2 = x + -2xX + -4xY

Reorder the terms:
4xY + -4xY + 4xy + -5y + 6y2 = x + -2xX + -4xY

Combine like terms: 4xY + -4xY = 0
0 + 4xy + -5y + 6y2 = x + -2xX + -4xY
4xy + -5y + 6y2 = x + -2xX + -4xY

Add '-4xy' to each side of the equation.
4xy + -5y + -4xy + 6y2 = x + -2xX + -4xY + -4xy

Reorder the terms:
4xy + -4xy + -5y + 6y2 = x + -2xX + -4xY + -4xy

Combine like terms: 4xy + -4xy = 0
0 + -5y + 6y2 = x + -2xX + -4xY + -4xy
-5y + 6y2 = x + -2xX + -4xY + -4xy

Add '5y' to each side of the equation.
-5y + 5y + 6y2 = x + -2xX + -4xY + -4xy + 5y

Combine like terms: -5y + 5y = 0
0 + 6y2 = x + -2xX + -4xY + -4xy + 5y
6y2 = x + -2xX + -4xY + -4xy + 5y

Add '-6y2' to each side of the equation.
6y2 + -6y2 = x + -2xX + -4xY + -4xy + 5y + -6y2

Combine like terms: 6y2 + -6y2 = 0
0 = x + -2xX + -4xY + -4xy + 5y + -6y2

Simplifying
0 = x + -2xX + -4xY + -4xy + 5y + -6y2

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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