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Simplifying (4xy + 3y2) * dx + (2x + 2y2) * dy = 0 Reorder the terms for easier multiplication: dx(4xy + 3y2) + (2x + 2y2) * dy = 0 (4xy * dx + 3y2 * dx) + (2x + 2y2) * dy = 0 Reorder the terms: (3dxy2 + 4dx2y) + (2x + 2y2) * dy = 0 (3dxy2 + 4dx2y) + (2x + 2y2) * dy = 0 Reorder the terms for easier multiplication: 3dxy2 + 4dx2y + dy(2x + 2y2) = 0 3dxy2 + 4dx2y + (2x * dy + 2y2 * dy) = 0 3dxy2 + 4dx2y + (2dxy + 2dy3) = 0 Reorder the terms: 2dxy + 3dxy2 + 4dx2y + 2dy3 = 0 Solving 2dxy + 3dxy2 + 4dx2y + 2dy3 = 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), 'dy'. dy(2x + 3xy + 4x2 + 2y2) = 0Subproblem 1
Set the factor 'dy' equal to zero and attempt to solve: Simplifying dy = 0 Solving dy = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dy = 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 '(2x + 3xy + 4x2 + 2y2)' equal to zero and attempt to solve: Simplifying 2x + 3xy + 4x2 + 2y2 = 0 Solving 2x + 3xy + 4x2 + 2y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-2x' to each side of the equation. 2x + 3xy + 4x2 + -2x + 2y2 = 0 + -2x Reorder the terms: 2x + -2x + 3xy + 4x2 + 2y2 = 0 + -2x Combine like terms: 2x + -2x = 0 0 + 3xy + 4x2 + 2y2 = 0 + -2x 3xy + 4x2 + 2y2 = 0 + -2x Remove the zero: 3xy + 4x2 + 2y2 = -2x Add '-3xy' to each side of the equation. 3xy + 4x2 + -3xy + 2y2 = -2x + -3xy Reorder the terms: 3xy + -3xy + 4x2 + 2y2 = -2x + -3xy Combine like terms: 3xy + -3xy = 0 0 + 4x2 + 2y2 = -2x + -3xy 4x2 + 2y2 = -2x + -3xy Add '-4x2' to each side of the equation. 4x2 + -4x2 + 2y2 = -2x + -3xy + -4x2 Combine like terms: 4x2 + -4x2 = 0 0 + 2y2 = -2x + -3xy + -4x2 2y2 = -2x + -3xy + -4x2 Add '-2y2' to each side of the equation. 2y2 + -2y2 = -2x + -3xy + -4x2 + -2y2 Combine like terms: 2y2 + -2y2 = 0 0 = -2x + -3xy + -4x2 + -2y2 Simplifying 0 = -2x + -3xy + -4x2 + -2y2 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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