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Simplifying (2xy + 2y2 + 2y) * dx + (2x2 + 6xy + 4x) * dy = 0 Reorder the terms: (2xy + 2y + 2y2) * dx + (2x2 + 6xy + 4x) * dy = 0 Reorder the terms for easier multiplication: dx(2xy + 2y + 2y2) + (2x2 + 6xy + 4x) * dy = 0 (2xy * dx + 2y * dx + 2y2 * dx) + (2x2 + 6xy + 4x) * dy = 0 Reorder the terms: (2dxy + 2dxy2 + 2dx2y) + (2x2 + 6xy + 4x) * dy = 0 (2dxy + 2dxy2 + 2dx2y) + (2x2 + 6xy + 4x) * dy = 0 Reorder the terms: 2dxy + 2dxy2 + 2dx2y + (4x + 6xy + 2x2) * dy = 0 Reorder the terms for easier multiplication: 2dxy + 2dxy2 + 2dx2y + dy(4x + 6xy + 2x2) = 0 2dxy + 2dxy2 + 2dx2y + (4x * dy + 6xy * dy + 2x2 * dy) = 0 2dxy + 2dxy2 + 2dx2y + (4dxy + 6dxy2 + 2dx2y) = 0 Reorder the terms: 2dxy + 4dxy + 2dxy2 + 6dxy2 + 2dx2y + 2dx2y = 0 Combine like terms: 2dxy + 4dxy = 6dxy 6dxy + 2dxy2 + 6dxy2 + 2dx2y + 2dx2y = 0 Combine like terms: 2dxy2 + 6dxy2 = 8dxy2 6dxy + 8dxy2 + 2dx2y + 2dx2y = 0 Combine like terms: 2dx2y + 2dx2y = 4dx2y 6dxy + 8dxy2 + 4dx2y = 0 Solving 6dxy + 8dxy2 + 4dx2y = 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), '2dxy'. 2dxy(3 + 4y + 2x) = 0 Ignore the factor 2.Subproblem 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 '(3 + 4y + 2x)' equal to zero and attempt to solve: Simplifying 3 + 4y + 2x = 0 Reorder the terms: 3 + 2x + 4y = 0 Solving 3 + 2x + 4y = 0 Move all terms containing d to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + 2x + -3 + 4y = 0 + -3 Reorder the terms: 3 + -3 + 2x + 4y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x + 4y = 0 + -3 2x + 4y = 0 + -3 Combine like terms: 0 + -3 = -3 2x + 4y = -3 Add '-2x' to each side of the equation. 2x + -2x + 4y = -3 + -2x Combine like terms: 2x + -2x = 0 0 + 4y = -3 + -2x 4y = -3 + -2x Add '-4y' to each side of the equation. 4y + -4y = -3 + -2x + -4y Combine like terms: 4y + -4y = 0 0 = -3 + -2x + -4y Simplifying 0 = -3 + -2x + -4y 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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