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Simplifying 2(x + 1) * dy + -1(x + 2 + -1xy2 + -2y2) * dx = 0 Reorder the terms: 2(1 + x) * dy + -1(x + 2 + -1xy2 + -2y2) * dx = 0 Reorder the terms for easier multiplication: 2dy(1 + x) + -1(x + 2 + -1xy2 + -2y2) * dx = 0 (1 * 2dy + x * 2dy) + -1(x + 2 + -1xy2 + -2y2) * dx = 0 Reorder the terms: (2dxy + 2dy) + -1(x + 2 + -1xy2 + -2y2) * dx = 0 (2dxy + 2dy) + -1(x + 2 + -1xy2 + -2y2) * dx = 0 Reorder the terms: 2dxy + 2dy + -1(2 + x + -1xy2 + -2y2) * dx = 0 Reorder the terms for easier multiplication: 2dxy + 2dy + -1dx(2 + x + -1xy2 + -2y2) = 0 2dxy + 2dy + (2 * -1dx + x * -1dx + -1xy2 * -1dx + -2y2 * -1dx) = 0 Reorder the terms: 2dxy + 2dy + (-2dx + 2dxy2 + -1dx2 + 1dx2y2) = 0 2dxy + 2dy + (-2dx + 2dxy2 + -1dx2 + 1dx2y2) = 0 Reorder the terms: -2dx + 2dxy + 2dxy2 + -1dx2 + 1dx2y2 + 2dy = 0 Solving -2dx + 2dxy + 2dxy2 + -1dx2 + 1dx2y2 + 2dy = 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 + 2xy + 2xy2 + -1x2 + x2y2 + 2y) = 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 + 2xy + 2xy2 + -1x2 + x2y2 + 2y)' equal to zero and attempt to solve: Simplifying -2x + 2xy + 2xy2 + -1x2 + x2y2 + 2y = 0 Solving -2x + 2xy + 2xy2 + -1x2 + x2y2 + 2y = 0 Move all terms containing d to the left, all other terms to the right. Add '2x' to each side of the equation. -2x + 2xy + 2xy2 + -1x2 + x2y2 + 2x + 2y = 0 + 2x Reorder the terms: -2x + 2x + 2xy + 2xy2 + -1x2 + x2y2 + 2y = 0 + 2x Combine like terms: -2x + 2x = 0 0 + 2xy + 2xy2 + -1x2 + x2y2 + 2y = 0 + 2x 2xy + 2xy2 + -1x2 + x2y2 + 2y = 0 + 2x Remove the zero: 2xy + 2xy2 + -1x2 + x2y2 + 2y = 2x Add '-2xy' to each side of the equation. 2xy + 2xy2 + -1x2 + x2y2 + -2xy + 2y = 2x + -2xy Reorder the terms: 2xy + -2xy + 2xy2 + -1x2 + x2y2 + 2y = 2x + -2xy Combine like terms: 2xy + -2xy = 0 0 + 2xy2 + -1x2 + x2y2 + 2y = 2x + -2xy 2xy2 + -1x2 + x2y2 + 2y = 2x + -2xy Add '-2xy2' to each side of the equation. 2xy2 + -1x2 + x2y2 + -2xy2 + 2y = 2x + -2xy + -2xy2 Reorder the terms: 2xy2 + -2xy2 + -1x2 + x2y2 + 2y = 2x + -2xy + -2xy2 Combine like terms: 2xy2 + -2xy2 = 0 0 + -1x2 + x2y2 + 2y = 2x + -2xy + -2xy2 -1x2 + x2y2 + 2y = 2x + -2xy + -2xy2 Add 'x2' to each side of the equation. -1x2 + x2y2 + x2 + 2y = 2x + -2xy + -2xy2 + x2 Reorder the terms: -1x2 + x2 + x2y2 + 2y = 2x + -2xy + -2xy2 + x2 Combine like terms: -1x2 + x2 = 0 0 + x2y2 + 2y = 2x + -2xy + -2xy2 + x2 x2y2 + 2y = 2x + -2xy + -2xy2 + x2 Add '-1x2y2' to each side of the equation. x2y2 + -1x2y2 + 2y = 2x + -2xy + -2xy2 + x2 + -1x2y2 Combine like terms: x2y2 + -1x2y2 = 0 0 + 2y = 2x + -2xy + -2xy2 + x2 + -1x2y2 2y = 2x + -2xy + -2xy2 + x2 + -1x2y2 Add '-2y' to each side of the equation. 2y + -2y = 2x + -2xy + -2xy2 + x2 + -1x2y2 + -2y Combine like terms: 2y + -2y = 0 0 = 2x + -2xy + -2xy2 + x2 + -1x2y2 + -2y Simplifying 0 = 2x + -2xy + -2xy2 + x2 + -1x2y2 + -2y 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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