(x-2y+3)dx+(2x-4y-3)DH=0

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Solution for (x-2y+3)dx+(2x-4y-3)DH=0 equation: 


Simplifying
(x + -2y + 3) * dx + (2x + -4y + -3) * DH = 0

Reorder the terms:
(3 + x + -2y) * dx + (2x + -4y + -3) * DH = 0

Reorder the terms for easier multiplication:
dx(3 + x + -2y) + (2x + -4y + -3) * DH = 0
(3 * dx + x * dx + -2y * dx) + (2x + -4y + -3) * DH = 0

Reorder the terms:
(3dx + -2dxy + dx2) + (2x + -4y + -3) * DH = 0
(3dx + -2dxy + dx2) + (2x + -4y + -3) * DH = 0

Reorder the terms:
3dx + -2dxy + dx2 + (-3 + 2x + -4y) * DH = 0

Reorder the terms for easier multiplication:
3dx + -2dxy + dx2 + DH(-3 + 2x + -4y) = 0
3dx + -2dxy + dx2 + (-3 * DH + 2x * DH + -4y * DH) = 0
3dx + -2dxy + dx2 + (-3DH + 2xDH + -4yDH) = 0

Reorder the terms:
-3DH + 3dx + -2dxy + dx2 + 2xDH + -4yDH = 0

Solving
-3DH + 3dx + -2dxy + dx2 + 2xDH + -4yDH = 0

Solving for variable 'D'.

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

Add '-3dx' to each side of the equation.
-3DH + 3dx + -2dxy + dx2 + 2xDH + -3dx + -4yDH = 0 + -3dx

Reorder the terms:
-3DH + 3dx + -3dx + -2dxy + dx2 + 2xDH + -4yDH = 0 + -3dx

Combine like terms: 3dx + -3dx = 0
-3DH + 0 + -2dxy + dx2 + 2xDH + -4yDH = 0 + -3dx
-3DH + -2dxy + dx2 + 2xDH + -4yDH = 0 + -3dx
Remove the zero:
-3DH + -2dxy + dx2 + 2xDH + -4yDH = -3dx

Add '2dxy' to each side of the equation.
-3DH + -2dxy + dx2 + 2xDH + 2dxy + -4yDH = -3dx + 2dxy

Reorder the terms:
-3DH + -2dxy + 2dxy + dx2 + 2xDH + -4yDH = -3dx + 2dxy

Combine like terms: -2dxy + 2dxy = 0
-3DH + 0 + dx2 + 2xDH + -4yDH = -3dx + 2dxy
-3DH + dx2 + 2xDH + -4yDH = -3dx + 2dxy

Add '-1dx2' to each side of the equation.
-3DH + dx2 + 2xDH + -1dx2 + -4yDH = -3dx + 2dxy + -1dx2

Reorder the terms:
-3DH + dx2 + -1dx2 + 2xDH + -4yDH = -3dx + 2dxy + -1dx2

Combine like terms: dx2 + -1dx2 = 0
-3DH + 0 + 2xDH + -4yDH = -3dx + 2dxy + -1dx2
-3DH + 2xDH + -4yDH = -3dx + 2dxy + -1dx2

Reorder the terms:
-3DH + 3dx + -2dxy + dx2 + 2xDH + -4yDH = -3dx + 2dxy + -1dx2 + 3dx + -2dxy + dx2

Reorder the terms:
-3DH + 3dx + -2dxy + dx2 + 2xDH + -4yDH = -3dx + 3dx + 2dxy + -2dxy + -1dx2 + dx2

Combine like terms: -3dx + 3dx = 0
-3DH + 3dx + -2dxy + dx2 + 2xDH + -4yDH = 0 + 2dxy + -2dxy + -1dx2 + dx2
-3DH + 3dx + -2dxy + dx2 + 2xDH + -4yDH = 2dxy + -2dxy + -1dx2 + dx2

Combine like terms: 2dxy + -2dxy = 0
-3DH + 3dx + -2dxy + dx2 + 2xDH + -4yDH = 0 + -1dx2 + dx2
-3DH + 3dx + -2dxy + dx2 + 2xDH + -4yDH = -1dx2 + dx2

Combine like terms: -1dx2 + dx2 = 0
-3DH + 3dx + -2dxy + dx2 + 2xDH + -4yDH = 0

The solution to this equation could not be determined.

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