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Simplifying (4x2 + 3xy + y * 2) * dx + (4y2 + 3xy + x2) * dy = 0 Reorder the terms for easier multiplication: (4x2 + 3xy + 2y) * dx + (4y2 + 3xy + x2) * dy = 0 Reorder the terms: (3xy + 4x2 + 2y) * dx + (4y2 + 3xy + x2) * dy = 0 Reorder the terms for easier multiplication: dx(3xy + 4x2 + 2y) + (4y2 + 3xy + x2) * dy = 0 (3xy * dx + 4x2 * dx + 2y * dx) + (4y2 + 3xy + x2) * dy = 0 Reorder the terms: (2dxy + 3dx2y + 4dx3) + (4y2 + 3xy + x2) * dy = 0 (2dxy + 3dx2y + 4dx3) + (4y2 + 3xy + x2) * dy = 0 Reorder the terms: 2dxy + 3dx2y + 4dx3 + (3xy + x2 + 4y2) * dy = 0 Reorder the terms for easier multiplication: 2dxy + 3dx2y + 4dx3 + dy(3xy + x2 + 4y2) = 0 2dxy + 3dx2y + 4dx3 + (3xy * dy + x2 * dy + 4y2 * dy) = 0 2dxy + 3dx2y + 4dx3 + (3dxy2 + dx2y + 4dy3) = 0 Reorder the terms: 2dxy + 3dxy2 + 3dx2y + dx2y + 4dx3 + 4dy3 = 0 Combine like terms: 3dx2y + dx2y = 4dx2y 2dxy + 3dxy2 + 4dx2y + 4dx3 + 4dy3 = 0 Solving 2dxy + 3dxy2 + 4dx2y + 4dx3 + 4dy3 = 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), 'd'. d(2xy + 3xy2 + 4x2y + 4x3 + 4y3) = 0Subproblem 1
Set the factor 'd' equal to zero and attempt to solve: Simplifying d = 0 Solving d = 0 Move all terms containing d to the left, all other terms to the right. Simplifying d = 0Subproblem 2
Set the factor '(2xy + 3xy2 + 4x2y + 4x3 + 4y3)' equal to zero and attempt to solve: Simplifying 2xy + 3xy2 + 4x2y + 4x3 + 4y3 = 0 Solving 2xy + 3xy2 + 4x2y + 4x3 + 4y3 = 0 Move all terms containing d to the left, all other terms to the right. Add '-2xy' to each side of the equation. 2xy + 3xy2 + 4x2y + 4x3 + -2xy + 4y3 = 0 + -2xy Reorder the terms: 2xy + -2xy + 3xy2 + 4x2y + 4x3 + 4y3 = 0 + -2xy Combine like terms: 2xy + -2xy = 0 0 + 3xy2 + 4x2y + 4x3 + 4y3 = 0 + -2xy 3xy2 + 4x2y + 4x3 + 4y3 = 0 + -2xy Remove the zero: 3xy2 + 4x2y + 4x3 + 4y3 = -2xy Add '-3xy2' to each side of the equation. 3xy2 + 4x2y + 4x3 + -3xy2 + 4y3 = -2xy + -3xy2 Reorder the terms: 3xy2 + -3xy2 + 4x2y + 4x3 + 4y3 = -2xy + -3xy2 Combine like terms: 3xy2 + -3xy2 = 0 0 + 4x2y + 4x3 + 4y3 = -2xy + -3xy2 4x2y + 4x3 + 4y3 = -2xy + -3xy2 Add '-4x2y' to each side of the equation. 4x2y + 4x3 + -4x2y + 4y3 = -2xy + -3xy2 + -4x2y Reorder the terms: 4x2y + -4x2y + 4x3 + 4y3 = -2xy + -3xy2 + -4x2y Combine like terms: 4x2y + -4x2y = 0 0 + 4x3 + 4y3 = -2xy + -3xy2 + -4x2y 4x3 + 4y3 = -2xy + -3xy2 + -4x2y Add '-4x3' to each side of the equation. 4x3 + -4x3 + 4y3 = -2xy + -3xy2 + -4x2y + -4x3 Combine like terms: 4x3 + -4x3 = 0 0 + 4y3 = -2xy + -3xy2 + -4x2y + -4x3 4y3 = -2xy + -3xy2 + -4x2y + -4x3 Add '-4y3' to each side of the equation. 4y3 + -4y3 = -2xy + -3xy2 + -4x2y + -4x3 + -4y3 Combine like terms: 4y3 + -4y3 = 0 0 = -2xy + -3xy2 + -4x2y + -4x3 + -4y3 Simplifying 0 = -2xy + -3xy2 + -4x2y + -4x3 + -4y3 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
d = {0}
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