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Simplifying (7x3 + 3x2 + 4y) * dx + (4x3 + x + 5y) * dy = 0 Reorder the terms: (3x2 + 7x3 + 4y) * dx + (4x3 + x + 5y) * dy = 0 Reorder the terms for easier multiplication: dx(3x2 + 7x3 + 4y) + (4x3 + x + 5y) * dy = 0 (3x2 * dx + 7x3 * dx + 4y * dx) + (4x3 + x + 5y) * dy = 0 Reorder the terms: (4dxy + 3dx3 + 7dx4) + (4x3 + x + 5y) * dy = 0 (4dxy + 3dx3 + 7dx4) + (4x3 + x + 5y) * dy = 0 Reorder the terms: 4dxy + 3dx3 + 7dx4 + (x + 4x3 + 5y) * dy = 0 Reorder the terms for easier multiplication: 4dxy + 3dx3 + 7dx4 + dy(x + 4x3 + 5y) = 0 4dxy + 3dx3 + 7dx4 + (x * dy + 4x3 * dy + 5y * dy) = 0 4dxy + 3dx3 + 7dx4 + (dxy + 4dx3y + 5dy2) = 0 Reorder the terms: 4dxy + dxy + 3dx3 + 4dx3y + 7dx4 + 5dy2 = 0 Combine like terms: 4dxy + dxy = 5dxy 5dxy + 3dx3 + 4dx3y + 7dx4 + 5dy2 = 0 Solving 5dxy + 3dx3 + 4dx3y + 7dx4 + 5dy2 = 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(5xy + 3x3 + 4x3y + 7x4 + 5y2) = 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 '(5xy + 3x3 + 4x3y + 7x4 + 5y2)' equal to zero and attempt to solve: Simplifying 5xy + 3x3 + 4x3y + 7x4 + 5y2 = 0 Solving 5xy + 3x3 + 4x3y + 7x4 + 5y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-5xy' to each side of the equation. 5xy + 3x3 + 4x3y + 7x4 + -5xy + 5y2 = 0 + -5xy Reorder the terms: 5xy + -5xy + 3x3 + 4x3y + 7x4 + 5y2 = 0 + -5xy Combine like terms: 5xy + -5xy = 0 0 + 3x3 + 4x3y + 7x4 + 5y2 = 0 + -5xy 3x3 + 4x3y + 7x4 + 5y2 = 0 + -5xy Remove the zero: 3x3 + 4x3y + 7x4 + 5y2 = -5xy Add '-3x3' to each side of the equation. 3x3 + 4x3y + 7x4 + -3x3 + 5y2 = -5xy + -3x3 Reorder the terms: 3x3 + -3x3 + 4x3y + 7x4 + 5y2 = -5xy + -3x3 Combine like terms: 3x3 + -3x3 = 0 0 + 4x3y + 7x4 + 5y2 = -5xy + -3x3 4x3y + 7x4 + 5y2 = -5xy + -3x3 Add '-4x3y' to each side of the equation. 4x3y + 7x4 + -4x3y + 5y2 = -5xy + -3x3 + -4x3y Reorder the terms: 4x3y + -4x3y + 7x4 + 5y2 = -5xy + -3x3 + -4x3y Combine like terms: 4x3y + -4x3y = 0 0 + 7x4 + 5y2 = -5xy + -3x3 + -4x3y 7x4 + 5y2 = -5xy + -3x3 + -4x3y Add '-7x4' to each side of the equation. 7x4 + -7x4 + 5y2 = -5xy + -3x3 + -4x3y + -7x4 Combine like terms: 7x4 + -7x4 = 0 0 + 5y2 = -5xy + -3x3 + -4x3y + -7x4 5y2 = -5xy + -3x3 + -4x3y + -7x4 Add '-5y2' to each side of the equation. 5y2 + -5y2 = -5xy + -3x3 + -4x3y + -7x4 + -5y2 Combine like terms: 5y2 + -5y2 = 0 0 = -5xy + -3x3 + -4x3y + -7x4 + -5y2 Simplifying 0 = -5xy + -3x3 + -4x3y + -7x4 + -5y2 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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