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Simplifying (x2 + 2y2) * dx + (2x2 + y2) * dy = 0 Reorder the terms for easier multiplication: dx(x2 + 2y2) + (2x2 + y2) * dy = 0 (x2 * dx + 2y2 * dx) + (2x2 + y2) * dy = 0 Reorder the terms: (2dxy2 + dx3) + (2x2 + y2) * dy = 0 (2dxy2 + dx3) + (2x2 + y2) * dy = 0 Reorder the terms for easier multiplication: 2dxy2 + dx3 + dy(2x2 + y2) = 0 2dxy2 + dx3 + (2x2 * dy + y2 * dy) = 0 2dxy2 + dx3 + (2dx2y + dy3) = 0 Reorder the terms: 2dxy2 + 2dx2y + dx3 + dy3 = 0 Solving 2dxy2 + 2dx2y + dx3 + 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(2xy2 + 2x2y + x3 + 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 '(2xy2 + 2x2y + x3 + y3)' equal to zero and attempt to solve: Simplifying 2xy2 + 2x2y + x3 + y3 = 0 Solving 2xy2 + 2x2y + x3 + y3 = 0 Move all terms containing d to the left, all other terms to the right. Add '-2xy2' to each side of the equation. 2xy2 + 2x2y + x3 + -2xy2 + y3 = 0 + -2xy2 Reorder the terms: 2xy2 + -2xy2 + 2x2y + x3 + y3 = 0 + -2xy2 Combine like terms: 2xy2 + -2xy2 = 0 0 + 2x2y + x3 + y3 = 0 + -2xy2 2x2y + x3 + y3 = 0 + -2xy2 Remove the zero: 2x2y + x3 + y3 = -2xy2 Add '-2x2y' to each side of the equation. 2x2y + x3 + -2x2y + y3 = -2xy2 + -2x2y Reorder the terms: 2x2y + -2x2y + x3 + y3 = -2xy2 + -2x2y Combine like terms: 2x2y + -2x2y = 0 0 + x3 + y3 = -2xy2 + -2x2y x3 + y3 = -2xy2 + -2x2y Add '-1x3' to each side of the equation. x3 + -1x3 + y3 = -2xy2 + -2x2y + -1x3 Combine like terms: x3 + -1x3 = 0 0 + y3 = -2xy2 + -2x2y + -1x3 y3 = -2xy2 + -2x2y + -1x3 Add '-1y3' to each side of the equation. y3 + -1y3 = -2xy2 + -2x2y + -1x3 + -1y3 Combine like terms: y3 + -1y3 = 0 0 = -2xy2 + -2x2y + -1x3 + -1y3 Simplifying 0 = -2xy2 + -2x2y + -1x3 + -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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