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Simplifying (3y + -2x + 1) * dx = (4x + -1y + 3) * dy Reorder the terms: (1 + -2x + 3y) * dx = (4x + -1y + 3) * dy Reorder the terms for easier multiplication: dx(1 + -2x + 3y) = (4x + -1y + 3) * dy (1 * dx + -2x * dx + 3y * dx) = (4x + -1y + 3) * dy Reorder the terms: (1dx + 3dxy + -2dx2) = (4x + -1y + 3) * dy (1dx + 3dxy + -2dx2) = (4x + -1y + 3) * dy Reorder the terms: 1dx + 3dxy + -2dx2 = (3 + 4x + -1y) * dy Reorder the terms for easier multiplication: 1dx + 3dxy + -2dx2 = dy(3 + 4x + -1y) 1dx + 3dxy + -2dx2 = (3 * dy + 4x * dy + -1y * dy) Reorder the terms: 1dx + 3dxy + -2dx2 = (4dxy + 3dy + -1dy2) 1dx + 3dxy + -2dx2 = (4dxy + 3dy + -1dy2) Solving 1dx + 3dxy + -2dx2 = 4dxy + 3dy + -1dy2 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-4dxy' to each side of the equation. 1dx + 3dxy + -4dxy + -2dx2 = 4dxy + 3dy + -4dxy + -1dy2 Combine like terms: 3dxy + -4dxy = -1dxy 1dx + -1dxy + -2dx2 = 4dxy + 3dy + -4dxy + -1dy2 Reorder the terms: 1dx + -1dxy + -2dx2 = 4dxy + -4dxy + 3dy + -1dy2 Combine like terms: 4dxy + -4dxy = 0 1dx + -1dxy + -2dx2 = 0 + 3dy + -1dy2 1dx + -1dxy + -2dx2 = 3dy + -1dy2 Add '-3dy' to each side of the equation. 1dx + -1dxy + -2dx2 + -3dy = 3dy + -3dy + -1dy2 Combine like terms: 3dy + -3dy = 0 1dx + -1dxy + -2dx2 + -3dy = 0 + -1dy2 1dx + -1dxy + -2dx2 + -3dy = -1dy2 Add 'dy2' to each side of the equation. 1dx + -1dxy + -2dx2 + -3dy + dy2 = -1dy2 + dy2 Combine like terms: -1dy2 + dy2 = 0 1dx + -1dxy + -2dx2 + -3dy + dy2 = 0 Factor out the Greatest Common Factor (GCF), 'd'. d(x + -1xy + -2x2 + -3y + y2) = 0Subproblem 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 = 0Subproblem 2
Set the factor '(x + -1xy + -2x2 + -3y + y2)' equal to zero and attempt to solve: Simplifying x + -1xy + -2x2 + -3y + y2 = 0 Solving x + -1xy + -2x2 + -3y + y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1xy + -2x2 + -3y + -1x + y2 = 0 + -1x Reorder the terms: x + -1x + -1xy + -2x2 + -3y + y2 = 0 + -1x Combine like terms: x + -1x = 0 0 + -1xy + -2x2 + -3y + y2 = 0 + -1x -1xy + -2x2 + -3y + y2 = 0 + -1x Remove the zero: -1xy + -2x2 + -3y + y2 = -1x Add 'xy' to each side of the equation. -1xy + -2x2 + -3y + xy + y2 = -1x + xy Reorder the terms: -1xy + xy + -2x2 + -3y + y2 = -1x + xy Combine like terms: -1xy + xy = 0 0 + -2x2 + -3y + y2 = -1x + xy -2x2 + -3y + y2 = -1x + xy Add '2x2' to each side of the equation. -2x2 + -3y + 2x2 + y2 = -1x + xy + 2x2 Reorder the terms: -2x2 + 2x2 + -3y + y2 = -1x + xy + 2x2 Combine like terms: -2x2 + 2x2 = 0 0 + -3y + y2 = -1x + xy + 2x2 -3y + y2 = -1x + xy + 2x2 Add '3y' to each side of the equation. -3y + 3y + y2 = -1x + xy + 2x2 + 3y Combine like terms: -3y + 3y = 0 0 + y2 = -1x + xy + 2x2 + 3y y2 = -1x + xy + 2x2 + 3y Add '-1y2' to each side of the equation. y2 + -1y2 = -1x + xy + 2x2 + 3y + -1y2 Combine like terms: y2 + -1y2 = 0 0 = -1x + xy + 2x2 + 3y + -1y2 Simplifying 0 = -1x + xy + 2x2 + 3y + -1y2 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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