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Simplifying (3x2y + y3) * dy + -1(x3 + 3xy2) * dx = 0 Reorder the terms for easier multiplication: dy(3x2y + y3) + -1(x3 + 3xy2) * dx = 0 (3x2y * dy + y3 * dy) + -1(x3 + 3xy2) * dx = 0 (3dx2y2 + dy4) + -1(x3 + 3xy2) * dx = 0 Reorder the terms: 3dx2y2 + dy4 + -1(3xy2 + x3) * dx = 0 Reorder the terms for easier multiplication: 3dx2y2 + dy4 + -1dx(3xy2 + x3) = 0 3dx2y2 + dy4 + (3xy2 * -1dx + x3 * -1dx) = 0 3dx2y2 + dy4 + (-3dx2y2 + -1dx4) = 0 Reorder the terms: 3dx2y2 + -3dx2y2 + -1dx4 + dy4 = 0 Combine like terms: 3dx2y2 + -3dx2y2 = 0 0 + -1dx4 + dy4 = 0 -1dx4 + dy4 = 0 Solving -1dx4 + dy4 = 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(-1x4 + y4) = 0 Factor a difference between two squares. d((x2 + y2)(-1x2 + y2)) = 0 Factor a difference between two squares. d((x2 + y2)((x + y)(-1x + y))) = 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 '(x2 + y2)' equal to zero and attempt to solve: Simplifying x2 + y2 = 0 Solving x2 + y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x2' to each side of the equation. x2 + -1x2 + y2 = 0 + -1x2 Combine like terms: x2 + -1x2 = 0 0 + y2 = 0 + -1x2 y2 = 0 + -1x2 Remove the zero: y2 = -1x2 Add '-1y2' to each side of the equation. y2 + -1y2 = -1x2 + -1y2 Combine like terms: y2 + -1y2 = 0 0 = -1x2 + -1y2 Simplifying 0 = -1x2 + -1y2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(x + y)' equal to zero and attempt to solve: Simplifying x + y = 0 Solving x + y = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x + y = 0 + -1x Combine like terms: x + -1x = 0 0 + y = 0 + -1x y = 0 + -1x Remove the zero: y = -1x Add '-1y' to each side of the equation. y + -1y = -1x + -1y Combine like terms: y + -1y = 0 0 = -1x + -1y Simplifying 0 = -1x + -1y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 4
Set the factor '(-1x + y)' equal to zero and attempt to solve: Simplifying -1x + y = 0 Solving -1x + y = 0 Move all terms containing d to the left, all other terms to the right. Add 'x' to each side of the equation. -1x + x + y = 0 + x Combine like terms: -1x + x = 0 0 + y = 0 + x y = 0 + x Remove the zero: y = x Add '-1y' to each side of the equation. y + -1y = x + -1y Combine like terms: y + -1y = 0 0 = x + -1y Simplifying 0 = x + -1y 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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