(3x+2y+y^2)+(2x+2xy+5y^2)dy=0

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Solution for (3x+2y+y^2)+(2x+2xy+5y^2)dy=0 equation: 


Simplifying
(3x + 2y + y2) + (2x + 2xy + 5y2) * dy = 0

Remove parenthesis around (3x + 2y + y2)
3x + 2y + y2 + (2x + 2xy + 5y2) * dy = 0

Reorder the terms for easier multiplication:
3x + 2y + y2 + dy(2x + 2xy + 5y2) = 0
3x + 2y + y2 + (2x * dy + 2xy * dy + 5y2 * dy) = 0
3x + 2y + y2 + (2dxy + 2dxy2 + 5dy3) = 0

Reorder the terms:
2dxy + 2dxy2 + 5dy3 + 3x + 2y + y2 = 0

Solving
2dxy + 2dxy2 + 5dy3 + 3x + 2y + y2 = 0

Solving for variable 'd'.

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

Add '-3x' to each side of the equation.
2dxy + 2dxy2 + 5dy3 + 3x + 2y + -3x + y2 = 0 + -3x

Reorder the terms:
2dxy + 2dxy2 + 5dy3 + 3x + -3x + 2y + y2 = 0 + -3x

Combine like terms: 3x + -3x = 0
2dxy + 2dxy2 + 5dy3 + 0 + 2y + y2 = 0 + -3x
2dxy + 2dxy2 + 5dy3 + 2y + y2 = 0 + -3x
Remove the zero:
2dxy + 2dxy2 + 5dy3 + 2y + y2 = -3x

Add '-2y' to each side of the equation.
2dxy + 2dxy2 + 5dy3 + 2y + -2y + y2 = -3x + -2y

Combine like terms: 2y + -2y = 0
2dxy + 2dxy2 + 5dy3 + 0 + y2 = -3x + -2y
2dxy + 2dxy2 + 5dy3 + y2 = -3x + -2y

Add '-1y2' to each side of the equation.
2dxy + 2dxy2 + 5dy3 + y2 + -1y2 = -3x + -2y + -1y2

Combine like terms: y2 + -1y2 = 0
2dxy + 2dxy2 + 5dy3 + 0 = -3x + -2y + -1y2
2dxy + 2dxy2 + 5dy3 = -3x + -2y + -1y2

Reorder the terms:
2dxy + 2dxy2 + 5dy3 + 3x + 2y + y2 = -3x + 3x + -2y + 2y + -1y2 + y2

Combine like terms: -3x + 3x = 0
2dxy + 2dxy2 + 5dy3 + 3x + 2y + y2 = 0 + -2y + 2y + -1y2 + y2
2dxy + 2dxy2 + 5dy3 + 3x + 2y + y2 = -2y + 2y + -1y2 + y2

Combine like terms: -2y + 2y = 0
2dxy + 2dxy2 + 5dy3 + 3x + 2y + y2 = 0 + -1y2 + y2
2dxy + 2dxy2 + 5dy3 + 3x + 2y + y2 = -1y2 + y2

Combine like terms: -1y2 + y2 = 0
2dxy + 2dxy2 + 5dy3 + 3x + 2y + y2 = 0

The solution to this equation could not be determined.

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