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

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


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

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

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

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

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

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

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

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

Solving for variable 'd'.

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

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

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

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

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'd'.
d(4x + -6xy + 2x2 + -1y + 2y2) = 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 '(4x + -6xy + 2x2 + -1y + 2y2)' equal to zero and attempt to solve: Simplifying 4x + -6xy + 2x2 + -1y + 2y2 = 0 Solving 4x + -6xy + 2x2 + -1y + 2y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-4x' to each side of the equation. 4x + -6xy + 2x2 + -1y + -4x + 2y2 = 0 + -4x Reorder the terms: 4x + -4x + -6xy + 2x2 + -1y + 2y2 = 0 + -4x Combine like terms: 4x + -4x = 0 0 + -6xy + 2x2 + -1y + 2y2 = 0 + -4x -6xy + 2x2 + -1y + 2y2 = 0 + -4x Remove the zero: -6xy + 2x2 + -1y + 2y2 = -4x Add '6xy' to each side of the equation. -6xy + 2x2 + -1y + 6xy + 2y2 = -4x + 6xy Reorder the terms: -6xy + 6xy + 2x2 + -1y + 2y2 = -4x + 6xy Combine like terms: -6xy + 6xy = 0 0 + 2x2 + -1y + 2y2 = -4x + 6xy 2x2 + -1y + 2y2 = -4x + 6xy Add '-2x2' to each side of the equation. 2x2 + -1y + -2x2 + 2y2 = -4x + 6xy + -2x2 Reorder the terms: 2x2 + -2x2 + -1y + 2y2 = -4x + 6xy + -2x2 Combine like terms: 2x2 + -2x2 = 0 0 + -1y + 2y2 = -4x + 6xy + -2x2 -1y + 2y2 = -4x + 6xy + -2x2 Add 'y' to each side of the equation. -1y + y + 2y2 = -4x + 6xy + -2x2 + y Combine like terms: -1y + y = 0 0 + 2y2 = -4x + 6xy + -2x2 + y 2y2 = -4x + 6xy + -2x2 + y Add '-2y2' to each side of the equation. 2y2 + -2y2 = -4x + 6xy + -2x2 + y + -2y2 Combine like terms: 2y2 + -2y2 = 0 0 = -4x + 6xy + -2x2 + y + -2y2 Simplifying 0 = -4x + 6xy + -2x2 + y + -2y2 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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