((y^2)-(2xy)+(6x))dx-((x^2)-(2xy)+(2))=0

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Solution for ((y^2)-(2xy)+(6x))dx-((x^2)-(2xy)+(2))=0 equation: 


Simplifying
((y2) + -1(2xy) + (6x)) * dx + -1((x2) + -1(2xy) + (2)) = 0
(y2 + -1(2xy) + (6x)) * dx + -1((x2) + -1(2xy) + (2)) = 0

Remove parenthesis around (2xy)
(y2 + -1 * 2xy + (6x)) * dx + -1((x2) + -1(2xy) + (2)) = 0

Multiply -1 * 2
(y2 + -2xy + (6x)) * dx + -1((x2) + -1(2xy) + (2)) = 0

Reorder the terms:
((6x) + -2xy + y2) * dx + -1((x2) + -1(2xy) + (2)) = 0

Reorder the terms for easier multiplication:
dx((6x) + -2xy + y2) + -1((x2) + -1(2xy) + (2)) = 0
((6x) * dx + -2xy * dx + y2 * dx) + -1((x2) + -1(2xy) + (2)) = 0

Reorder the terms:
(dxy2 + 6dx2 + -2dx2y) + -1((x2) + -1(2xy) + (2)) = 0
(dxy2 + 6dx2 + -2dx2y) + -1((x2) + -1(2xy) + (2)) = 0
dxy2 + 6dx2 + -2dx2y + -1(x2 + -1(2xy) + (2)) = 0

Remove parenthesis around (2xy)
dxy2 + 6dx2 + -2dx2y + -1(x2 + -1 * 2xy + (2)) = 0

Multiply -1 * 2
dxy2 + 6dx2 + -2dx2y + -1(x2 + -2xy + (2)) = 0
dxy2 + 6dx2 + -2dx2y + -1(x2 + -2xy + 2) = 0

Reorder the terms:
dxy2 + 6dx2 + -2dx2y + -1(2 + -2xy + x2) = 0
dxy2 + 6dx2 + -2dx2y + (2 * -1 + -2xy * -1 + x2 * -1) = 0
dxy2 + 6dx2 + -2dx2y + (-2 + 2xy + -1x2) = 0

Reorder the terms:
-2 + dxy2 + 6dx2 + -2dx2y + 2xy + -1x2 = 0

Solving
-2 + dxy2 + 6dx2 + -2dx2y + 2xy + -1x2 = 0

Solving for variable 'd'.

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

Add '2' to each side of the equation.
-2 + dxy2 + 6dx2 + -2dx2y + 2xy + 2 + -1x2 = 0 + 2

Reorder the terms:
-2 + 2 + dxy2 + 6dx2 + -2dx2y + 2xy + -1x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + dxy2 + 6dx2 + -2dx2y + 2xy + -1x2 = 0 + 2
dxy2 + 6dx2 + -2dx2y + 2xy + -1x2 = 0 + 2

Combine like terms: 0 + 2 = 2
dxy2 + 6dx2 + -2dx2y + 2xy + -1x2 = 2

Add '-2xy' to each side of the equation.
dxy2 + 6dx2 + -2dx2y + 2xy + -2xy + -1x2 = 2 + -2xy

Combine like terms: 2xy + -2xy = 0
dxy2 + 6dx2 + -2dx2y + 0 + -1x2 = 2 + -2xy
dxy2 + 6dx2 + -2dx2y + -1x2 = 2 + -2xy

Add 'x2' to each side of the equation.
dxy2 + 6dx2 + -2dx2y + -1x2 + x2 = 2 + -2xy + x2

Combine like terms: -1x2 + x2 = 0
dxy2 + 6dx2 + -2dx2y + 0 = 2 + -2xy + x2
dxy2 + 6dx2 + -2dx2y = 2 + -2xy + x2

Reorder the terms:
-2 + dxy2 + 6dx2 + -2dx2y + 2xy + -1x2 = 2 + -2xy + x2 + -2 + 2xy + -1x2

Reorder the terms:
-2 + dxy2 + 6dx2 + -2dx2y + 2xy + -1x2 = 2 + -2 + -2xy + 2xy + x2 + -1x2

Combine like terms: 2 + -2 = 0
-2 + dxy2 + 6dx2 + -2dx2y + 2xy + -1x2 = 0 + -2xy + 2xy + x2 + -1x2
-2 + dxy2 + 6dx2 + -2dx2y + 2xy + -1x2 = -2xy + 2xy + x2 + -1x2

Combine like terms: -2xy + 2xy = 0
-2 + dxy2 + 6dx2 + -2dx2y + 2xy + -1x2 = 0 + x2 + -1x2
-2 + dxy2 + 6dx2 + -2dx2y + 2xy + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-2 + dxy2 + 6dx2 + -2dx2y + 2xy + -1x2 = 0

The solution to this equation could not be determined.

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