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Simplifying (4x3 + -8xy2 + 2) * dx + (4y3 + -8x2) * dy = 0 Reorder the terms: (2 + -8xy2 + 4x3) * dx + (4y3 + -8x2) * dy = 0 Reorder the terms for easier multiplication: dx(2 + -8xy2 + 4x3) + (4y3 + -8x2) * dy = 0 (2 * dx + -8xy2 * dx + 4x3 * dx) + (4y3 + -8x2) * dy = 0 (2dx + -8dx2y2 + 4dx4) + (4y3 + -8x2) * dy = 0 Reorder the terms: 2dx + -8dx2y2 + 4dx4 + (-8x2 + 4y3) * dy = 0 Reorder the terms for easier multiplication: 2dx + -8dx2y2 + 4dx4 + dy(-8x2 + 4y3) = 0 2dx + -8dx2y2 + 4dx4 + (-8x2 * dy + 4y3 * dy) = 0 2dx + -8dx2y2 + 4dx4 + (-8dx2y + 4dy4) = 0 Reorder the terms: 2dx + -8dx2y + -8dx2y2 + 4dx4 + 4dy4 = 0 Solving 2dx + -8dx2y + -8dx2y2 + 4dx4 + 4dy4 = 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), '2d'. 2d(x + -4x2y + -4x2y2 + 2x4 + 2y4) = 0 Ignore the factor 2.Subproblem 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 '(x + -4x2y + -4x2y2 + 2x4 + 2y4)' equal to zero and attempt to solve: Simplifying x + -4x2y + -4x2y2 + 2x4 + 2y4 = 0 Solving x + -4x2y + -4x2y2 + 2x4 + 2y4 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -4x2y + -4x2y2 + 2x4 + -1x + 2y4 = 0 + -1x Reorder the terms: x + -1x + -4x2y + -4x2y2 + 2x4 + 2y4 = 0 + -1x Combine like terms: x + -1x = 0 0 + -4x2y + -4x2y2 + 2x4 + 2y4 = 0 + -1x -4x2y + -4x2y2 + 2x4 + 2y4 = 0 + -1x Remove the zero: -4x2y + -4x2y2 + 2x4 + 2y4 = -1x Add '4x2y' to each side of the equation. -4x2y + -4x2y2 + 2x4 + 4x2y + 2y4 = -1x + 4x2y Reorder the terms: -4x2y + 4x2y + -4x2y2 + 2x4 + 2y4 = -1x + 4x2y Combine like terms: -4x2y + 4x2y = 0 0 + -4x2y2 + 2x4 + 2y4 = -1x + 4x2y -4x2y2 + 2x4 + 2y4 = -1x + 4x2y Add '4x2y2' to each side of the equation. -4x2y2 + 2x4 + 4x2y2 + 2y4 = -1x + 4x2y + 4x2y2 Reorder the terms: -4x2y2 + 4x2y2 + 2x4 + 2y4 = -1x + 4x2y + 4x2y2 Combine like terms: -4x2y2 + 4x2y2 = 0 0 + 2x4 + 2y4 = -1x + 4x2y + 4x2y2 2x4 + 2y4 = -1x + 4x2y + 4x2y2 Add '-2x4' to each side of the equation. 2x4 + -2x4 + 2y4 = -1x + 4x2y + 4x2y2 + -2x4 Combine like terms: 2x4 + -2x4 = 0 0 + 2y4 = -1x + 4x2y + 4x2y2 + -2x4 2y4 = -1x + 4x2y + 4x2y2 + -2x4 Add '-2y4' to each side of the equation. 2y4 + -2y4 = -1x + 4x2y + 4x2y2 + -2x4 + -2y4 Combine like terms: 2y4 + -2y4 = 0 0 = -1x + 4x2y + 4x2y2 + -2x4 + -2y4 Simplifying 0 = -1x + 4x2y + 4x2y2 + -2x4 + -2y4 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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