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Simplifying (2y2 + 3xy) * dx + (3xy + 4x2) * dy = 0 Reorder the terms: (3xy + 2y2) * dx + (3xy + 4x2) * dy = 0 Reorder the terms for easier multiplication: dx(3xy + 2y2) + (3xy + 4x2) * dy = 0 (3xy * dx + 2y2 * dx) + (3xy + 4x2) * dy = 0 Reorder the terms: (2dxy2 + 3dx2y) + (3xy + 4x2) * dy = 0 (2dxy2 + 3dx2y) + (3xy + 4x2) * dy = 0 Reorder the terms for easier multiplication: 2dxy2 + 3dx2y + dy(3xy + 4x2) = 0 2dxy2 + 3dx2y + (3xy * dy + 4x2 * dy) = 0 2dxy2 + 3dx2y + (3dxy2 + 4dx2y) = 0 Reorder the terms: 2dxy2 + 3dxy2 + 3dx2y + 4dx2y = 0 Combine like terms: 2dxy2 + 3dxy2 = 5dxy2 5dxy2 + 3dx2y + 4dx2y = 0 Combine like terms: 3dx2y + 4dx2y = 7dx2y 5dxy2 + 7dx2y = 0 Solving 5dxy2 + 7dx2y = 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(5y + 7x) = 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 '(5y + 7x)' equal to zero and attempt to solve: Simplifying 5y + 7x = 0 Reorder the terms: 7x + 5y = 0 Solving 7x + 5y = 0 Move all terms containing d to the left, all other terms to the right. Add '-7x' to each side of the equation. 7x + -7x + 5y = 0 + -7x Combine like terms: 7x + -7x = 0 0 + 5y = 0 + -7x 5y = 0 + -7x Remove the zero: 5y = -7x Add '-5y' to each side of the equation. 5y + -5y = -7x + -5y Combine like terms: 5y + -5y = 0 0 = -7x + -5y Simplifying 0 = -7x + -5y 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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