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Simplifying (4x3 + -6xy2) * dx + (4y3 + -6xy) * dy = 0 Reorder the terms: (-6xy2 + 4x3) * dx + (4y3 + -6xy) * dy = 0 Reorder the terms for easier multiplication: dx(-6xy2 + 4x3) + (4y3 + -6xy) * dy = 0 (-6xy2 * dx + 4x3 * dx) + (4y3 + -6xy) * dy = 0 (-6dx2y2 + 4dx4) + (4y3 + -6xy) * dy = 0 Reorder the terms: -6dx2y2 + 4dx4 + (-6xy + 4y3) * dy = 0 Reorder the terms for easier multiplication: -6dx2y2 + 4dx4 + dy(-6xy + 4y3) = 0 -6dx2y2 + 4dx4 + (-6xy * dy + 4y3 * dy) = 0 -6dx2y2 + 4dx4 + (-6dxy2 + 4dy4) = 0 Reorder the terms: -6dxy2 + -6dx2y2 + 4dx4 + 4dy4 = 0 Solving -6dxy2 + -6dx2y2 + 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(-3xy2 + -3x2y2 + 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 '(-3xy2 + -3x2y2 + 2x4 + 2y4)' equal to zero and attempt to solve: Simplifying -3xy2 + -3x2y2 + 2x4 + 2y4 = 0 Solving -3xy2 + -3x2y2 + 2x4 + 2y4 = 0 Move all terms containing d to the left, all other terms to the right. Add '3xy2' to each side of the equation. -3xy2 + -3x2y2 + 2x4 + 3xy2 + 2y4 = 0 + 3xy2 Reorder the terms: -3xy2 + 3xy2 + -3x2y2 + 2x4 + 2y4 = 0 + 3xy2 Combine like terms: -3xy2 + 3xy2 = 0 0 + -3x2y2 + 2x4 + 2y4 = 0 + 3xy2 -3x2y2 + 2x4 + 2y4 = 0 + 3xy2 Remove the zero: -3x2y2 + 2x4 + 2y4 = 3xy2 Add '3x2y2' to each side of the equation. -3x2y2 + 2x4 + 3x2y2 + 2y4 = 3xy2 + 3x2y2 Reorder the terms: -3x2y2 + 3x2y2 + 2x4 + 2y4 = 3xy2 + 3x2y2 Combine like terms: -3x2y2 + 3x2y2 = 0 0 + 2x4 + 2y4 = 3xy2 + 3x2y2 2x4 + 2y4 = 3xy2 + 3x2y2 Add '-2x4' to each side of the equation. 2x4 + -2x4 + 2y4 = 3xy2 + 3x2y2 + -2x4 Combine like terms: 2x4 + -2x4 = 0 0 + 2y4 = 3xy2 + 3x2y2 + -2x4 2y4 = 3xy2 + 3x2y2 + -2x4 Add '-2y4' to each side of the equation. 2y4 + -2y4 = 3xy2 + 3x2y2 + -2x4 + -2y4 Combine like terms: 2y4 + -2y4 = 0 0 = 3xy2 + 3x2y2 + -2x4 + -2y4 Simplifying 0 = 3xy2 + 3x2y2 + -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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