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Simplifying (4xy2 + 6y) * dx + (5x2y + 8x) * dy = 0 Reorder the terms for easier multiplication: dx(4xy2 + 6y) + (5x2y + 8x) * dy = 0 (4xy2 * dx + 6y * dx) + (5x2y + 8x) * dy = 0 Reorder the terms: (6dxy + 4dx2y2) + (5x2y + 8x) * dy = 0 (6dxy + 4dx2y2) + (5x2y + 8x) * dy = 0 Reorder the terms: 6dxy + 4dx2y2 + (8x + 5x2y) * dy = 0 Reorder the terms for easier multiplication: 6dxy + 4dx2y2 + dy(8x + 5x2y) = 0 6dxy + 4dx2y2 + (8x * dy + 5x2y * dy) = 0 6dxy + 4dx2y2 + (8dxy + 5dx2y2) = 0 Reorder the terms: 6dxy + 8dxy + 4dx2y2 + 5dx2y2 = 0 Combine like terms: 6dxy + 8dxy = 14dxy 14dxy + 4dx2y2 + 5dx2y2 = 0 Combine like terms: 4dx2y2 + 5dx2y2 = 9dx2y2 14dxy + 9dx2y2 = 0 Solving 14dxy + 9dx2y2 = 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), 'dxy'. dxy(14 + 9xy) = 0Subproblem 1
Set the factor 'dxy' equal to zero and attempt to solve: Simplifying dxy = 0 Solving dxy = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dxy = 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 '(14 + 9xy)' equal to zero and attempt to solve: Simplifying 14 + 9xy = 0 Solving 14 + 9xy = 0 Move all terms containing d to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + 9xy = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 9xy = 0 + -14 9xy = 0 + -14 Combine like terms: 0 + -14 = -14 9xy = -14 Add '-9xy' to each side of the equation. 9xy + -9xy = -14 + -9xy Combine like terms: 9xy + -9xy = 0 0 = -14 + -9xy Simplifying 0 = -14 + -9xy 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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