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Simplifying (x3 + -3xy2) * dx = (y3 + -3x2y) * dy Reorder the terms: (-3xy2 + x3) * dx = (y3 + -3x2y) * dy Reorder the terms for easier multiplication: dx(-3xy2 + x3) = (y3 + -3x2y) * dy (-3xy2 * dx + x3 * dx) = (y3 + -3x2y) * dy (-3dx2y2 + dx4) = (y3 + -3x2y) * dy Reorder the terms: -3dx2y2 + dx4 = (-3x2y + y3) * dy Reorder the terms for easier multiplication: -3dx2y2 + dx4 = dy(-3x2y + y3) -3dx2y2 + dx4 = (-3x2y * dy + y3 * dy) -3dx2y2 + dx4 = (-3dx2y2 + dy4) Add '3dx2y2' to each side of the equation. -3dx2y2 + 3dx2y2 + dx4 = -3dx2y2 + 3dx2y2 + dy4 Combine like terms: -3dx2y2 + 3dx2y2 = 0 0 + dx4 = -3dx2y2 + 3dx2y2 + dy4 dx4 = -3dx2y2 + 3dx2y2 + dy4 Combine like terms: -3dx2y2 + 3dx2y2 = 0 dx4 = 0 + dy4 dx4 = dy4 Solving dx4 = dy4 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1dy4' to each side of the equation. dx4 + -1dy4 = dy4 + -1dy4 Combine like terms: dy4 + -1dy4 = 0 dx4 + -1dy4 = 0 Factor out the Greatest Common Factor (GCF), 'd'. d(x4 + -1y4) = 0 Factor a difference between two squares. d((x2 + y2)(x2 + -1y2)) = 0 Factor a difference between two squares. d((x2 + y2)((x + y)(x + -1y))) = 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 '(x + -1y)' equal to zero and attempt to solve: Simplifying x + -1y = 0 Solving x + -1y = 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 + -1y = 0 + -1x Combine like terms: x + -1x = 0 0 + -1y = 0 + -1x -1y = 0 + -1x Remove the zero: -1y = -1x Add 'y' to each side of the equation. -1y + y = -1x + y Combine like terms: -1y + y = 0 0 = -1x + y Simplifying 0 = -1x + y 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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