(2x-3y+1)dx=-(6x+4y-3)dy

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Solution for (2x-3y+1)dx=-(6x+4y-3)dy equation:


Simplifying
(2x + -3y + 1) * dx = -1(6x + 4y + -3) * dy

Reorder the terms:
(1 + 2x + -3y) * dx = -1(6x + 4y + -3) * dy

Reorder the terms for easier multiplication:
dx(1 + 2x + -3y) = -1(6x + 4y + -3) * dy
(1 * dx + 2x * dx + -3y * dx) = -1(6x + 4y + -3) * dy

Reorder the terms:
(1dx + -3dxy + 2dx2) = -1(6x + 4y + -3) * dy
(1dx + -3dxy + 2dx2) = -1(6x + 4y + -3) * dy

Reorder the terms:
1dx + -3dxy + 2dx2 = -1(-3 + 6x + 4y) * dy

Reorder the terms for easier multiplication:
1dx + -3dxy + 2dx2 = -1dy(-3 + 6x + 4y)
1dx + -3dxy + 2dx2 = (-3 * -1dy + 6x * -1dy + 4y * -1dy)

Reorder the terms:
1dx + -3dxy + 2dx2 = (-6dxy + 3dy + -4dy2)
1dx + -3dxy + 2dx2 = (-6dxy + 3dy + -4dy2)

Solving
1dx + -3dxy + 2dx2 = -6dxy + 3dy + -4dy2

Solving for variable 'd'.

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

Add '6dxy' to each side of the equation.
1dx + -3dxy + 6dxy + 2dx2 = -6dxy + 3dy + 6dxy + -4dy2

Combine like terms: -3dxy + 6dxy = 3dxy
1dx + 3dxy + 2dx2 = -6dxy + 3dy + 6dxy + -4dy2

Reorder the terms:
1dx + 3dxy + 2dx2 = -6dxy + 6dxy + 3dy + -4dy2

Combine like terms: -6dxy + 6dxy = 0
1dx + 3dxy + 2dx2 = 0 + 3dy + -4dy2
1dx + 3dxy + 2dx2 = 3dy + -4dy2

Add '-3dy' to each side of the equation.
1dx + 3dxy + 2dx2 + -3dy = 3dy + -3dy + -4dy2

Combine like terms: 3dy + -3dy = 0
1dx + 3dxy + 2dx2 + -3dy = 0 + -4dy2
1dx + 3dxy + 2dx2 + -3dy = -4dy2

Add '4dy2' to each side of the equation.
1dx + 3dxy + 2dx2 + -3dy + 4dy2 = -4dy2 + 4dy2

Combine like terms: -4dy2 + 4dy2 = 0
1dx + 3dxy + 2dx2 + -3dy + 4dy2 = 0

Factor out the Greatest Common Factor (GCF), 'd'.
d(x + 3xy + 2x2 + -3y + 4y2) = 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 '(x + 3xy + 2x2 + -3y + 4y2)' equal to zero and attempt to solve: Simplifying x + 3xy + 2x2 + -3y + 4y2 = 0 Solving x + 3xy + 2x2 + -3y + 4y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + 3xy + 2x2 + -3y + -1x + 4y2 = 0 + -1x Reorder the terms: x + -1x + 3xy + 2x2 + -3y + 4y2 = 0 + -1x Combine like terms: x + -1x = 0 0 + 3xy + 2x2 + -3y + 4y2 = 0 + -1x 3xy + 2x2 + -3y + 4y2 = 0 + -1x Remove the zero: 3xy + 2x2 + -3y + 4y2 = -1x Add '-3xy' to each side of the equation. 3xy + 2x2 + -3y + -3xy + 4y2 = -1x + -3xy Reorder the terms: 3xy + -3xy + 2x2 + -3y + 4y2 = -1x + -3xy Combine like terms: 3xy + -3xy = 0 0 + 2x2 + -3y + 4y2 = -1x + -3xy 2x2 + -3y + 4y2 = -1x + -3xy Add '-2x2' to each side of the equation. 2x2 + -3y + -2x2 + 4y2 = -1x + -3xy + -2x2 Reorder the terms: 2x2 + -2x2 + -3y + 4y2 = -1x + -3xy + -2x2 Combine like terms: 2x2 + -2x2 = 0 0 + -3y + 4y2 = -1x + -3xy + -2x2 -3y + 4y2 = -1x + -3xy + -2x2 Add '3y' to each side of the equation. -3y + 3y + 4y2 = -1x + -3xy + -2x2 + 3y Combine like terms: -3y + 3y = 0 0 + 4y2 = -1x + -3xy + -2x2 + 3y 4y2 = -1x + -3xy + -2x2 + 3y Add '-4y2' to each side of the equation. 4y2 + -4y2 = -1x + -3xy + -2x2 + 3y + -4y2 Combine like terms: 4y2 + -4y2 = 0 0 = -1x + -3xy + -2x2 + 3y + -4y2 Simplifying 0 = -1x + -3xy + -2x2 + 3y + -4y2 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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