(3x+2)(y^2+4)dx-4y(x^2+5x+6)dy=0

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Solution for (3x+2)(y^2+4)dx-4y(x^2+5x+6)dy=0 equation:


Simplifying
(3x + 2)(y2 + 4) * dx + -4y(x2 + 5x + 6) * dy = 0

Reorder the terms:
(2 + 3x)(y2 + 4) * dx + -4y(x2 + 5x + 6) * dy = 0

Reorder the terms:
(2 + 3x)(4 + y2) * dx + -4y(x2 + 5x + 6) * dy = 0

Reorder the terms for easier multiplication:
dx(2 + 3x)(4 + y2) + -4y(x2 + 5x + 6) * dy = 0

Multiply (2 + 3x) * (4 + y2)
dx(2(4 + y2) + 3x * (4 + y2)) + -4y(x2 + 5x + 6) * dy = 0
dx((4 * 2 + y2 * 2) + 3x * (4 + y2)) + -4y(x2 + 5x + 6) * dy = 0
dx((8 + 2y2) + 3x * (4 + y2)) + -4y(x2 + 5x + 6) * dy = 0
dx(8 + 2y2 + (4 * 3x + y2 * 3x)) + -4y(x2 + 5x + 6) * dy = 0
dx(8 + 2y2 + (12x + 3xy2)) + -4y(x2 + 5x + 6) * dy = 0

Reorder the terms:
dx(8 + 12x + 3xy2 + 2y2) + -4y(x2 + 5x + 6) * dy = 0
dx(8 + 12x + 3xy2 + 2y2) + -4y(x2 + 5x + 6) * dy = 0
(8 * dx + 12x * dx + 3xy2 * dx + 2y2 * dx) + -4y(x2 + 5x + 6) * dy = 0

Reorder the terms:
(8dx + 2dxy2 + 12dx2 + 3dx2y2) + -4y(x2 + 5x + 6) * dy = 0
(8dx + 2dxy2 + 12dx2 + 3dx2y2) + -4y(x2 + 5x + 6) * dy = 0

Reorder the terms:
8dx + 2dxy2 + 12dx2 + 3dx2y2 + -4y(6 + 5x + x2) * dy = 0

Reorder the terms for easier multiplication:
8dx + 2dxy2 + 12dx2 + 3dx2y2 + -4y * dy(6 + 5x + x2) = 0

Multiply y * dy
8dx + 2dxy2 + 12dx2 + 3dx2y2 + -4dy2(6 + 5x + x2) = 0
8dx + 2dxy2 + 12dx2 + 3dx2y2 + (6 * -4dy2 + 5x * -4dy2 + x2 * -4dy2) = 0

Reorder the terms:
8dx + 2dxy2 + 12dx2 + 3dx2y2 + (-20dxy2 + -4dx2y2 + -24dy2) = 0
8dx + 2dxy2 + 12dx2 + 3dx2y2 + (-20dxy2 + -4dx2y2 + -24dy2) = 0

Reorder the terms:
8dx + 2dxy2 + -20dxy2 + 12dx2 + 3dx2y2 + -4dx2y2 + -24dy2 = 0

Combine like terms: 2dxy2 + -20dxy2 = -18dxy2
8dx + -18dxy2 + 12dx2 + 3dx2y2 + -4dx2y2 + -24dy2 = 0

Combine like terms: 3dx2y2 + -4dx2y2 = -1dx2y2
8dx + -18dxy2 + 12dx2 + -1dx2y2 + -24dy2 = 0

Solving
8dx + -18dxy2 + 12dx2 + -1dx2y2 + -24dy2 = 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(8x + -18xy2 + 12x2 + -1x2y2 + -24y2) = 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 '(8x + -18xy2 + 12x2 + -1x2y2 + -24y2)' equal to zero and attempt to solve: Simplifying 8x + -18xy2 + 12x2 + -1x2y2 + -24y2 = 0 Solving 8x + -18xy2 + 12x2 + -1x2y2 + -24y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-8x' to each side of the equation. 8x + -18xy2 + 12x2 + -1x2y2 + -8x + -24y2 = 0 + -8x Reorder the terms: 8x + -8x + -18xy2 + 12x2 + -1x2y2 + -24y2 = 0 + -8x Combine like terms: 8x + -8x = 0 0 + -18xy2 + 12x2 + -1x2y2 + -24y2 = 0 + -8x -18xy2 + 12x2 + -1x2y2 + -24y2 = 0 + -8x Remove the zero: -18xy2 + 12x2 + -1x2y2 + -24y2 = -8x Add '18xy2' to each side of the equation. -18xy2 + 12x2 + -1x2y2 + 18xy2 + -24y2 = -8x + 18xy2 Reorder the terms: -18xy2 + 18xy2 + 12x2 + -1x2y2 + -24y2 = -8x + 18xy2 Combine like terms: -18xy2 + 18xy2 = 0 0 + 12x2 + -1x2y2 + -24y2 = -8x + 18xy2 12x2 + -1x2y2 + -24y2 = -8x + 18xy2 Add '-12x2' to each side of the equation. 12x2 + -1x2y2 + -12x2 + -24y2 = -8x + 18xy2 + -12x2 Reorder the terms: 12x2 + -12x2 + -1x2y2 + -24y2 = -8x + 18xy2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 0 + -1x2y2 + -24y2 = -8x + 18xy2 + -12x2 -1x2y2 + -24y2 = -8x + 18xy2 + -12x2 Add 'x2y2' to each side of the equation. -1x2y2 + x2y2 + -24y2 = -8x + 18xy2 + -12x2 + x2y2 Combine like terms: -1x2y2 + x2y2 = 0 0 + -24y2 = -8x + 18xy2 + -12x2 + x2y2 -24y2 = -8x + 18xy2 + -12x2 + x2y2 Add '24y2' to each side of the equation. -24y2 + 24y2 = -8x + 18xy2 + -12x2 + x2y2 + 24y2 Combine like terms: -24y2 + 24y2 = 0 0 = -8x + 18xy2 + -12x2 + x2y2 + 24y2 Simplifying 0 = -8x + 18xy2 + -12x2 + x2y2 + 24y2 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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