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Simplifying 2x(x + y + 2) * dx + (y2 + -1x2 + -4x + -1) * dy = 0 Reorder the terms: 2x(2 + x + y) * dx + (y2 + -1x2 + -4x + -1) * dy = 0 Reorder the terms for easier multiplication: 2x * dx(2 + x + y) + (y2 + -1x2 + -4x + -1) * dy = 0 Multiply x * dx 2dx2(2 + x + y) + (y2 + -1x2 + -4x + -1) * dy = 0 (2 * 2dx2 + x * 2dx2 + y * 2dx2) + (y2 + -1x2 + -4x + -1) * dy = 0 Reorder the terms: (4dx2 + 2dx2y + 2dx3) + (y2 + -1x2 + -4x + -1) * dy = 0 (4dx2 + 2dx2y + 2dx3) + (y2 + -1x2 + -4x + -1) * dy = 0 Reorder the terms: 4dx2 + 2dx2y + 2dx3 + (-1 + -4x + -1x2 + y2) * dy = 0 Reorder the terms for easier multiplication: 4dx2 + 2dx2y + 2dx3 + dy(-1 + -4x + -1x2 + y2) = 0 4dx2 + 2dx2y + 2dx3 + (-1 * dy + -4x * dy + -1x2 * dy + y2 * dy) = 0 Reorder the terms: 4dx2 + 2dx2y + 2dx3 + (-4dxy + -1dx2y + -1dy + dy3) = 0 4dx2 + 2dx2y + 2dx3 + (-4dxy + -1dx2y + -1dy + dy3) = 0 Reorder the terms: -4dxy + 4dx2 + 2dx2y + -1dx2y + 2dx3 + -1dy + dy3 = 0 Combine like terms: 2dx2y + -1dx2y = 1dx2y -4dxy + 4dx2 + 1dx2y + 2dx3 + -1dy + dy3 = 0 Solving -4dxy + 4dx2 + 1dx2y + 2dx3 + -1dy + dy3 = 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(-4xy + 4x2 + x2y + 2x3 + -1y + y3) = 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 '(-4xy + 4x2 + x2y + 2x3 + -1y + y3)' equal to zero and attempt to solve: Simplifying -4xy + 4x2 + x2y + 2x3 + -1y + y3 = 0 Solving -4xy + 4x2 + x2y + 2x3 + -1y + y3 = 0 Move all terms containing d to the left, all other terms to the right. Add '4xy' to each side of the equation. -4xy + 4x2 + x2y + 2x3 + -1y + 4xy + y3 = 0 + 4xy Reorder the terms: -4xy + 4xy + 4x2 + x2y + 2x3 + -1y + y3 = 0 + 4xy Combine like terms: -4xy + 4xy = 0 0 + 4x2 + x2y + 2x3 + -1y + y3 = 0 + 4xy 4x2 + x2y + 2x3 + -1y + y3 = 0 + 4xy Remove the zero: 4x2 + x2y + 2x3 + -1y + y3 = 4xy Add '-4x2' to each side of the equation. 4x2 + x2y + 2x3 + -1y + -4x2 + y3 = 4xy + -4x2 Reorder the terms: 4x2 + -4x2 + x2y + 2x3 + -1y + y3 = 4xy + -4x2 Combine like terms: 4x2 + -4x2 = 0 0 + x2y + 2x3 + -1y + y3 = 4xy + -4x2 x2y + 2x3 + -1y + y3 = 4xy + -4x2 Add '-1x2y' to each side of the equation. x2y + 2x3 + -1y + -1x2y + y3 = 4xy + -4x2 + -1x2y Reorder the terms: x2y + -1x2y + 2x3 + -1y + y3 = 4xy + -4x2 + -1x2y Combine like terms: x2y + -1x2y = 0 0 + 2x3 + -1y + y3 = 4xy + -4x2 + -1x2y 2x3 + -1y + y3 = 4xy + -4x2 + -1x2y Add '-2x3' to each side of the equation. 2x3 + -1y + -2x3 + y3 = 4xy + -4x2 + -1x2y + -2x3 Reorder the terms: 2x3 + -2x3 + -1y + y3 = 4xy + -4x2 + -1x2y + -2x3 Combine like terms: 2x3 + -2x3 = 0 0 + -1y + y3 = 4xy + -4x2 + -1x2y + -2x3 -1y + y3 = 4xy + -4x2 + -1x2y + -2x3 Add 'y' to each side of the equation. -1y + y + y3 = 4xy + -4x2 + -1x2y + -2x3 + y Combine like terms: -1y + y = 0 0 + y3 = 4xy + -4x2 + -1x2y + -2x3 + y y3 = 4xy + -4x2 + -1x2y + -2x3 + y Add '-1y3' to each side of the equation. y3 + -1y3 = 4xy + -4x2 + -1x2y + -2x3 + y + -1y3 Combine like terms: y3 + -1y3 = 0 0 = 4xy + -4x2 + -1x2y + -2x3 + y + -1y3 Simplifying 0 = 4xy + -4x2 + -1x2y + -2x3 + y + -1y3 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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