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

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


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

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

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

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

Multiply dx * dy
d2xy(1 + X + y)(-1 + 2x + 2y) = 0

Multiply (1 + X + y) * (-1 + 2x + 2y)
d2xy(1(-1 + 2x + 2y) + X(-1 + 2x + 2y) + y(-1 + 2x + 2y)) = 0
d2xy((-1 * 1 + 2x * 1 + 2y * 1) + X(-1 + 2x + 2y) + y(-1 + 2x + 2y)) = 0
d2xy((-1 + 2x + 2y) + X(-1 + 2x + 2y) + y(-1 + 2x + 2y)) = 0
d2xy(-1 + 2x + 2y + (-1 * X + 2x * X + 2y * X) + y(-1 + 2x + 2y)) = 0
d2xy(-1 + 2x + 2y + (-1X + 2xX + 2yX) + y(-1 + 2x + 2y)) = 0
d2xy(-1 + 2x + 2y + -1X + 2xX + 2yX + (-1 * y + 2x * y + 2y * y)) = 0

Reorder the terms:
d2xy(-1 + 2x + 2y + -1X + 2xX + 2yX + (2xy + -1y + 2y2)) = 0
d2xy(-1 + 2x + 2y + -1X + 2xX + 2yX + (2xy + -1y + 2y2)) = 0

Reorder the terms:
d2xy(-1 + -1X + 2x + 2xX + 2xy + 2y + -1y + 2yX + 2y2) = 0

Combine like terms: 2y + -1y = 1y
d2xy(-1 + -1X + 2x + 2xX + 2xy + 1y + 2yX + 2y2) = 0
(-1 * d2xy + -1X * d2xy + 2x * d2xy + 2xX * d2xy + 2xy * d2xy + 1y * d2xy + 2yX * d2xy + 2y2 * d2xy) = 0

Reorder the terms:
(-1d2xy + -1d2xyX + 1d2xy2 + 2d2xy2X + 2d2xy3 + 2d2x2y + 2d2x2yX + 2d2x2y2) = 0
(-1d2xy + -1d2xyX + 1d2xy2 + 2d2xy2X + 2d2xy3 + 2d2x2y + 2d2x2yX + 2d2x2y2) = 0

Solving
-1d2xy + -1d2xyX + 1d2xy2 + 2d2xy2X + 2d2xy3 + 2d2x2y + 2d2x2yX + 2d2x2y2 = 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), 'd2xy'.
d2xy(-1 + -1X + y + 2yX + 2y2 + 2x + 2xX + 2xy) = 0

Subproblem 1

Set the factor 'd2xy' equal to zero and attempt to solve: Simplifying d2xy = 0 Solving d2xy = 0 Move all terms containing d to the left, all other terms to the right. Simplifying d2xy = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(-1 + -1X + y + 2yX + 2y2 + 2x + 2xX + 2xy)' equal to zero and attempt to solve: Simplifying -1 + -1X + y + 2yX + 2y2 + 2x + 2xX + 2xy = 0 Reorder the terms: -1 + -1X + 2x + 2xX + 2xy + y + 2yX + 2y2 = 0 Solving -1 + -1X + 2x + 2xX + 2xy + y + 2yX + 2y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '1' to each side of the equation. -1 + -1X + 2x + 2xX + 2xy + y + 2yX + 1 + 2y2 = 0 + 1 Reorder the terms: -1 + 1 + -1X + 2x + 2xX + 2xy + y + 2yX + 2y2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1X + 2x + 2xX + 2xy + y + 2yX + 2y2 = 0 + 1 -1X + 2x + 2xX + 2xy + y + 2yX + 2y2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1X + 2x + 2xX + 2xy + y + 2yX + 2y2 = 1 Add 'X' to each side of the equation. -1X + 2x + 2xX + 2xy + y + 2yX + X + 2y2 = 1 + X Reorder the terms: -1X + X + 2x + 2xX + 2xy + y + 2yX + 2y2 = 1 + X Combine like terms: -1X + X = 0 0 + 2x + 2xX + 2xy + y + 2yX + 2y2 = 1 + X 2x + 2xX + 2xy + y + 2yX + 2y2 = 1 + X Add '-2x' to each side of the equation. 2x + 2xX + 2xy + y + 2yX + -2x + 2y2 = 1 + X + -2x Reorder the terms: 2x + -2x + 2xX + 2xy + y + 2yX + 2y2 = 1 + X + -2x Combine like terms: 2x + -2x = 0 0 + 2xX + 2xy + y + 2yX + 2y2 = 1 + X + -2x 2xX + 2xy + y + 2yX + 2y2 = 1 + X + -2x Add '-2xX' to each side of the equation. 2xX + 2xy + y + 2yX + -2xX + 2y2 = 1 + X + -2x + -2xX Reorder the terms: 2xX + -2xX + 2xy + y + 2yX + 2y2 = 1 + X + -2x + -2xX Combine like terms: 2xX + -2xX = 0 0 + 2xy + y + 2yX + 2y2 = 1 + X + -2x + -2xX 2xy + y + 2yX + 2y2 = 1 + X + -2x + -2xX Add '-2xy' to each side of the equation. 2xy + y + 2yX + -2xy + 2y2 = 1 + X + -2x + -2xX + -2xy Reorder the terms: 2xy + -2xy + y + 2yX + 2y2 = 1 + X + -2x + -2xX + -2xy Combine like terms: 2xy + -2xy = 0 0 + y + 2yX + 2y2 = 1 + X + -2x + -2xX + -2xy y + 2yX + 2y2 = 1 + X + -2x + -2xX + -2xy Add '-1y' to each side of the equation. y + 2yX + -1y + 2y2 = 1 + X + -2x + -2xX + -2xy + -1y Reorder the terms: y + -1y + 2yX + 2y2 = 1 + X + -2x + -2xX + -2xy + -1y Combine like terms: y + -1y = 0 0 + 2yX + 2y2 = 1 + X + -2x + -2xX + -2xy + -1y 2yX + 2y2 = 1 + X + -2x + -2xX + -2xy + -1y Add '-2yX' to each side of the equation. 2yX + -2yX + 2y2 = 1 + X + -2x + -2xX + -2xy + -1y + -2yX Combine like terms: 2yX + -2yX = 0 0 + 2y2 = 1 + X + -2x + -2xX + -2xy + -1y + -2yX 2y2 = 1 + X + -2x + -2xX + -2xy + -1y + -2yX Add '-2y2' to each side of the equation. 2y2 + -2y2 = 1 + X + -2x + -2xX + -2xy + -1y + -2yX + -2y2 Combine like terms: 2y2 + -2y2 = 0 0 = 1 + X + -2x + -2xX + -2xy + -1y + -2yX + -2y2 Simplifying 0 = 1 + X + -2x + -2xX + -2xy + -1y + -2yX + -2y2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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