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Simplifying (2y2 + 4x2y) * dx + (3x2 + 4xy) * dy = 0 Reorder the terms: (4x2y + 2y2) * dx + (3x2 + 4xy) * dy = 0 Reorder the terms for easier multiplication: dx(4x2y + 2y2) + (3x2 + 4xy) * dy = 0 (4x2y * dx + 2y2 * dx) + (3x2 + 4xy) * dy = 0 Reorder the terms: (2dxy2 + 4dx3y) + (3x2 + 4xy) * dy = 0 (2dxy2 + 4dx3y) + (3x2 + 4xy) * dy = 0 Reorder the terms: 2dxy2 + 4dx3y + (4xy + 3x2) * dy = 0 Reorder the terms for easier multiplication: 2dxy2 + 4dx3y + dy(4xy + 3x2) = 0 2dxy2 + 4dx3y + (4xy * dy + 3x2 * dy) = 0 2dxy2 + 4dx3y + (4dxy2 + 3dx2y) = 0 Reorder the terms: 2dxy2 + 4dxy2 + 3dx2y + 4dx3y = 0 Combine like terms: 2dxy2 + 4dxy2 = 6dxy2 6dxy2 + 3dx2y + 4dx3y = 0 Solving 6dxy2 + 3dx2y + 4dx3y = 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(6y + 3x + 4x2) = 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 '(6y + 3x + 4x2)' equal to zero and attempt to solve: Simplifying 6y + 3x + 4x2 = 0 Reorder the terms: 3x + 4x2 + 6y = 0 Solving 3x + 4x2 + 6y = 0 Move all terms containing d to the left, all other terms to the right. Add '-3x' to each side of the equation. 3x + 4x2 + -3x + 6y = 0 + -3x Reorder the terms: 3x + -3x + 4x2 + 6y = 0 + -3x Combine like terms: 3x + -3x = 0 0 + 4x2 + 6y = 0 + -3x 4x2 + 6y = 0 + -3x Remove the zero: 4x2 + 6y = -3x Add '-4x2' to each side of the equation. 4x2 + -4x2 + 6y = -3x + -4x2 Combine like terms: 4x2 + -4x2 = 0 0 + 6y = -3x + -4x2 6y = -3x + -4x2 Add '-6y' to each side of the equation. 6y + -6y = -3x + -4x2 + -6y Combine like terms: 6y + -6y = 0 0 = -3x + -4x2 + -6y Simplifying 0 = -3x + -4x2 + -6y 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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