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Simplifying (4xy2 + y) * dx + (6y3 + -1x) * dy = 0 Reorder the terms for easier multiplication: dx(4xy2 + y) + (6y3 + -1x) * dy = 0 (4xy2 * dx + y * dx) + (6y3 + -1x) * dy = 0 Reorder the terms: (dxy + 4dx2y2) + (6y3 + -1x) * dy = 0 (dxy + 4dx2y2) + (6y3 + -1x) * dy = 0 Reorder the terms: dxy + 4dx2y2 + (-1x + 6y3) * dy = 0 Reorder the terms for easier multiplication: dxy + 4dx2y2 + dy(-1x + 6y3) = 0 dxy + 4dx2y2 + (-1x * dy + 6y3 * dy) = 0 dxy + 4dx2y2 + (-1dxy + 6dy4) = 0 Reorder the terms: dxy + -1dxy + 4dx2y2 + 6dy4 = 0 Combine like terms: dxy + -1dxy = 0 0 + 4dx2y2 + 6dy4 = 0 4dx2y2 + 6dy4 = 0 Solving 4dx2y2 + 6dy4 = 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), '2dy2'. 2dy2(2x2 + 3y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'dy2' equal to zero and attempt to solve: Simplifying dy2 = 0 Solving dy2 = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dy2 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(2x2 + 3y2)' equal to zero and attempt to solve: Simplifying 2x2 + 3y2 = 0 Solving 2x2 + 3y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-2x2' to each side of the equation. 2x2 + -2x2 + 3y2 = 0 + -2x2 Combine like terms: 2x2 + -2x2 = 0 0 + 3y2 = 0 + -2x2 3y2 = 0 + -2x2 Remove the zero: 3y2 = -2x2 Add '-3y2' to each side of the equation. 3y2 + -3y2 = -2x2 + -3y2 Combine like terms: 3y2 + -3y2 = 0 0 = -2x2 + -3y2 Simplifying 0 = -2x2 + -3y2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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