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Simplifying (3x * y2 + 3y) * dx + (3(x2) * y + 3x) * dy = 0 Multiply x * y2 (3xy2 + 3y) * dx + (3(x2) * y + 3x) * dy = 0 Reorder the terms for easier multiplication: dx(3xy2 + 3y) + (3(x2) * y + 3x) * dy = 0 (3xy2 * dx + 3y * dx) + (3(x2) * y + 3x) * dy = 0 Reorder the terms: (3dxy + 3dx2y2) + (3(x2) * y + 3x) * dy = 0 (3dxy + 3dx2y2) + (3(x2) * y + 3x) * dy = 0 Multiply x2 * y 3dxy + 3dx2y2 + (3x2y + 3x) * dy = 0 Reorder the terms: 3dxy + 3dx2y2 + (3x + 3x2y) * dy = 0 Reorder the terms for easier multiplication: 3dxy + 3dx2y2 + dy(3x + 3x2y) = 0 3dxy + 3dx2y2 + (3x * dy + 3x2y * dy) = 0 3dxy + 3dx2y2 + (3dxy + 3dx2y2) = 0 Reorder the terms: 3dxy + 3dxy + 3dx2y2 + 3dx2y2 = 0 Combine like terms: 3dxy + 3dxy = 6dxy 6dxy + 3dx2y2 + 3dx2y2 = 0 Combine like terms: 3dx2y2 + 3dx2y2 = 6dx2y2 6dxy + 6dx2y2 = 0 Solving 6dxy + 6dx2y2 = 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), '6dxy'. 6dxy(1 + xy) = 0 Ignore the factor 6.Subproblem 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 '(1 + xy)' equal to zero and attempt to solve: Simplifying 1 + xy = 0 Solving 1 + xy = 0 Move all terms containing d to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + xy = 0 + -1 Combine like terms: 1 + -1 = 0 0 + xy = 0 + -1 xy = 0 + -1 Combine like terms: 0 + -1 = -1 xy = -1 Add '-1xy' to each side of the equation. xy + -1xy = -1 + -1xy Combine like terms: xy + -1xy = 0 0 = -1 + -1xy Simplifying 0 = -1 + -1xy 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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