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Simplifying (y2 + -2y + -3) * dx + (2xy + 6x + -2y + -6) * dy = 0 Reorder the terms: (-3 + -2y + y2) * dx + (2xy + 6x + -2y + -6) * dy = 0 Reorder the terms for easier multiplication: dx(-3 + -2y + y2) + (2xy + 6x + -2y + -6) * dy = 0 (-3 * dx + -2y * dx + y2 * dx) + (2xy + 6x + -2y + -6) * dy = 0 (-3dx + -2dxy + dxy2) + (2xy + 6x + -2y + -6) * dy = 0 Reorder the terms: -3dx + -2dxy + dxy2 + (-6 + 6x + 2xy + -2y) * dy = 0 Reorder the terms for easier multiplication: -3dx + -2dxy + dxy2 + dy(-6 + 6x + 2xy + -2y) = 0 -3dx + -2dxy + dxy2 + (-6 * dy + 6x * dy + 2xy * dy + -2y * dy) = 0 Reorder the terms: -3dx + -2dxy + dxy2 + (6dxy + 2dxy2 + -6dy + -2dy2) = 0 -3dx + -2dxy + dxy2 + (6dxy + 2dxy2 + -6dy + -2dy2) = 0 Reorder the terms: -3dx + -2dxy + 6dxy + dxy2 + 2dxy2 + -6dy + -2dy2 = 0 Combine like terms: -2dxy + 6dxy = 4dxy -3dx + 4dxy + dxy2 + 2dxy2 + -6dy + -2dy2 = 0 Combine like terms: dxy2 + 2dxy2 = 3dxy2 -3dx + 4dxy + 3dxy2 + -6dy + -2dy2 = 0 Solving -3dx + 4dxy + 3dxy2 + -6dy + -2dy2 = 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(-3x + 4xy + 3xy2 + -6y + -2y2) = 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 '(-3x + 4xy + 3xy2 + -6y + -2y2)' equal to zero and attempt to solve: Simplifying -3x + 4xy + 3xy2 + -6y + -2y2 = 0 Solving -3x + 4xy + 3xy2 + -6y + -2y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '3x' to each side of the equation. -3x + 4xy + 3xy2 + -6y + 3x + -2y2 = 0 + 3x Reorder the terms: -3x + 3x + 4xy + 3xy2 + -6y + -2y2 = 0 + 3x Combine like terms: -3x + 3x = 0 0 + 4xy + 3xy2 + -6y + -2y2 = 0 + 3x 4xy + 3xy2 + -6y + -2y2 = 0 + 3x Remove the zero: 4xy + 3xy2 + -6y + -2y2 = 3x Add '-4xy' to each side of the equation. 4xy + 3xy2 + -6y + -4xy + -2y2 = 3x + -4xy Reorder the terms: 4xy + -4xy + 3xy2 + -6y + -2y2 = 3x + -4xy Combine like terms: 4xy + -4xy = 0 0 + 3xy2 + -6y + -2y2 = 3x + -4xy 3xy2 + -6y + -2y2 = 3x + -4xy Add '-3xy2' to each side of the equation. 3xy2 + -6y + -3xy2 + -2y2 = 3x + -4xy + -3xy2 Reorder the terms: 3xy2 + -3xy2 + -6y + -2y2 = 3x + -4xy + -3xy2 Combine like terms: 3xy2 + -3xy2 = 0 0 + -6y + -2y2 = 3x + -4xy + -3xy2 -6y + -2y2 = 3x + -4xy + -3xy2 Add '6y' to each side of the equation. -6y + 6y + -2y2 = 3x + -4xy + -3xy2 + 6y Combine like terms: -6y + 6y = 0 0 + -2y2 = 3x + -4xy + -3xy2 + 6y -2y2 = 3x + -4xy + -3xy2 + 6y Add '2y2' to each side of the equation. -2y2 + 2y2 = 3x + -4xy + -3xy2 + 6y + 2y2 Combine like terms: -2y2 + 2y2 = 0 0 = 3x + -4xy + -3xy2 + 6y + 2y2 Simplifying 0 = 3x + -4xy + -3xy2 + 6y + 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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