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Simplifying (xy + 2x + y + 2) * dx + (x2 + 2x + 3) * dy = 0 Reorder the terms: (2 + 2x + xy + y) * dx + (x2 + 2x + 3) * dy = 0 Reorder the terms for easier multiplication: dx(2 + 2x + xy + y) + (x2 + 2x + 3) * dy = 0 (2 * dx + 2x * dx + xy * dx + y * dx) + (x2 + 2x + 3) * dy = 0 Reorder the terms: (2dx + dxy + 2dx2 + dx2y) + (x2 + 2x + 3) * dy = 0 (2dx + dxy + 2dx2 + dx2y) + (x2 + 2x + 3) * dy = 0 Reorder the terms: 2dx + dxy + 2dx2 + dx2y + (3 + 2x + x2) * dy = 0 Reorder the terms for easier multiplication: 2dx + dxy + 2dx2 + dx2y + dy(3 + 2x + x2) = 0 2dx + dxy + 2dx2 + dx2y + (3 * dy + 2x * dy + x2 * dy) = 0 Reorder the terms: 2dx + dxy + 2dx2 + dx2y + (2dxy + dx2y + 3dy) = 0 2dx + dxy + 2dx2 + dx2y + (2dxy + dx2y + 3dy) = 0 Reorder the terms: 2dx + dxy + 2dxy + 2dx2 + dx2y + dx2y + 3dy = 0 Combine like terms: dxy + 2dxy = 3dxy 2dx + 3dxy + 2dx2 + dx2y + dx2y + 3dy = 0 Combine like terms: dx2y + dx2y = 2dx2y 2dx + 3dxy + 2dx2 + 2dx2y + 3dy = 0 Solving 2dx + 3dxy + 2dx2 + 2dx2y + 3dy = 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(2x + 3xy + 2x2 + 2x2y + 3y) = 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 '(2x + 3xy + 2x2 + 2x2y + 3y)' equal to zero and attempt to solve: Simplifying 2x + 3xy + 2x2 + 2x2y + 3y = 0 Solving 2x + 3xy + 2x2 + 2x2y + 3y = 0 Move all terms containing d to the left, all other terms to the right. Add '-2x' to each side of the equation. 2x + 3xy + 2x2 + 2x2y + -2x + 3y = 0 + -2x Reorder the terms: 2x + -2x + 3xy + 2x2 + 2x2y + 3y = 0 + -2x Combine like terms: 2x + -2x = 0 0 + 3xy + 2x2 + 2x2y + 3y = 0 + -2x 3xy + 2x2 + 2x2y + 3y = 0 + -2x Remove the zero: 3xy + 2x2 + 2x2y + 3y = -2x Add '-3xy' to each side of the equation. 3xy + 2x2 + 2x2y + -3xy + 3y = -2x + -3xy Reorder the terms: 3xy + -3xy + 2x2 + 2x2y + 3y = -2x + -3xy Combine like terms: 3xy + -3xy = 0 0 + 2x2 + 2x2y + 3y = -2x + -3xy 2x2 + 2x2y + 3y = -2x + -3xy Add '-2x2' to each side of the equation. 2x2 + 2x2y + -2x2 + 3y = -2x + -3xy + -2x2 Reorder the terms: 2x2 + -2x2 + 2x2y + 3y = -2x + -3xy + -2x2 Combine like terms: 2x2 + -2x2 = 0 0 + 2x2y + 3y = -2x + -3xy + -2x2 2x2y + 3y = -2x + -3xy + -2x2 Add '-2x2y' to each side of the equation. 2x2y + -2x2y + 3y = -2x + -3xy + -2x2 + -2x2y Combine like terms: 2x2y + -2x2y = 0 0 + 3y = -2x + -3xy + -2x2 + -2x2y 3y = -2x + -3xy + -2x2 + -2x2y Add '-3y' to each side of the equation. 3y + -3y = -2x + -3xy + -2x2 + -2x2y + -3y Combine like terms: 3y + -3y = 0 0 = -2x + -3xy + -2x2 + -2x2y + -3y Simplifying 0 = -2x + -3xy + -2x2 + -2x2y + -3y 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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