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Simplifying (3y2 + -1x) * dx + (2y3 + -6y) * dy = 0 Reorder the terms: (-1x + 3y2) * dx + (2y3 + -6y) * dy = 0 Reorder the terms for easier multiplication: dx(-1x + 3y2) + (2y3 + -6y) * dy = 0 (-1x * dx + 3y2 * dx) + (2y3 + -6y) * dy = 0 Reorder the terms: (3dxy2 + -1dx2) + (2y3 + -6y) * dy = 0 (3dxy2 + -1dx2) + (2y3 + -6y) * dy = 0 Reorder the terms: 3dxy2 + -1dx2 + (-6y + 2y3) * dy = 0 Reorder the terms for easier multiplication: 3dxy2 + -1dx2 + dy(-6y + 2y3) = 0 3dxy2 + -1dx2 + (-6y * dy + 2y3 * dy) = 0 3dxy2 + -1dx2 + (-6dy2 + 2dy4) = 0 Solving 3dxy2 + -1dx2 + -6dy2 + 2dy4 = 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(3xy2 + -1x2 + -6y2 + 2y4) = 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 '(3xy2 + -1x2 + -6y2 + 2y4)' equal to zero and attempt to solve: Simplifying 3xy2 + -1x2 + -6y2 + 2y4 = 0 Solving 3xy2 + -1x2 + -6y2 + 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 + -1x2 + -6y2 + -3xy2 + 2y4 = 0 + -3xy2 Reorder the terms: 3xy2 + -3xy2 + -1x2 + -6y2 + 2y4 = 0 + -3xy2 Combine like terms: 3xy2 + -3xy2 = 0 0 + -1x2 + -6y2 + 2y4 = 0 + -3xy2 -1x2 + -6y2 + 2y4 = 0 + -3xy2 Remove the zero: -1x2 + -6y2 + 2y4 = -3xy2 Add 'x2' to each side of the equation. -1x2 + -6y2 + x2 + 2y4 = -3xy2 + x2 Reorder the terms: -1x2 + x2 + -6y2 + 2y4 = -3xy2 + x2 Combine like terms: -1x2 + x2 = 0 0 + -6y2 + 2y4 = -3xy2 + x2 -6y2 + 2y4 = -3xy2 + x2 Add '6y2' to each side of the equation. -6y2 + 6y2 + 2y4 = -3xy2 + x2 + 6y2 Combine like terms: -6y2 + 6y2 = 0 0 + 2y4 = -3xy2 + x2 + 6y2 2y4 = -3xy2 + x2 + 6y2 Add '-2y4' to each side of the equation. 2y4 + -2y4 = -3xy2 + x2 + 6y2 + -2y4 Combine like terms: 2y4 + -2y4 = 0 0 = -3xy2 + x2 + 6y2 + -2y4 Simplifying 0 = -3xy2 + x2 + 6y2 + -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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