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Simplifying (3xy2 + 2y) * dx + (3x2y + 2x) * dy = 0 Reorder the terms for easier multiplication: dx(3xy2 + 2y) + (3x2y + 2x) * dy = 0 (3xy2 * dx + 2y * dx) + (3x2y + 2x) * dy = 0 Reorder the terms: (2dxy + 3dx2y2) + (3x2y + 2x) * dy = 0 (2dxy + 3dx2y2) + (3x2y + 2x) * dy = 0 Reorder the terms: 2dxy + 3dx2y2 + (2x + 3x2y) * dy = 0 Reorder the terms for easier multiplication: 2dxy + 3dx2y2 + dy(2x + 3x2y) = 0 2dxy + 3dx2y2 + (2x * dy + 3x2y * dy) = 0 2dxy + 3dx2y2 + (2dxy + 3dx2y2) = 0 Reorder the terms: 2dxy + 2dxy + 3dx2y2 + 3dx2y2 = 0 Combine like terms: 2dxy + 2dxy = 4dxy 4dxy + 3dx2y2 + 3dx2y2 = 0 Combine like terms: 3dx2y2 + 3dx2y2 = 6dx2y2 4dxy + 6dx2y2 = 0 Solving 4dxy + 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), '2dxy'. 2dxy(2 + 3xy) = 0 Ignore the factor 2.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 '(2 + 3xy)' equal to zero and attempt to solve: Simplifying 2 + 3xy = 0 Solving 2 + 3xy = 0 Move all terms containing d to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 3xy = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3xy = 0 + -2 3xy = 0 + -2 Combine like terms: 0 + -2 = -2 3xy = -2 Add '-3xy' to each side of the equation. 3xy + -3xy = -2 + -3xy Combine like terms: 3xy + -3xy = 0 0 = -2 + -3xy Simplifying 0 = -2 + -3xy 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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