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Simplifying (3xy2 + 2y) * dx + (4x2y + 3x) * dy = 0 Reorder the terms for easier multiplication: dx(3xy2 + 2y) + (4x2y + 3x) * dy = 0 (3xy2 * dx + 2y * dx) + (4x2y + 3x) * dy = 0 Reorder the terms: (2dxy + 3dx2y2) + (4x2y + 3x) * dy = 0 (2dxy + 3dx2y2) + (4x2y + 3x) * dy = 0 Reorder the terms: 2dxy + 3dx2y2 + (3x + 4x2y) * dy = 0 Reorder the terms for easier multiplication: 2dxy + 3dx2y2 + dy(3x + 4x2y) = 0 2dxy + 3dx2y2 + (3x * dy + 4x2y * dy) = 0 2dxy + 3dx2y2 + (3dxy + 4dx2y2) = 0 Reorder the terms: 2dxy + 3dxy + 3dx2y2 + 4dx2y2 = 0 Combine like terms: 2dxy + 3dxy = 5dxy 5dxy + 3dx2y2 + 4dx2y2 = 0 Combine like terms: 3dx2y2 + 4dx2y2 = 7dx2y2 5dxy + 7dx2y2 = 0 Solving 5dxy + 7dx2y2 = 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(5 + 7xy) = 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 '(5 + 7xy)' equal to zero and attempt to solve: Simplifying 5 + 7xy = 0 Solving 5 + 7xy = 0 Move all terms containing d to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 7xy = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 7xy = 0 + -5 7xy = 0 + -5 Combine like terms: 0 + -5 = -5 7xy = -5 Add '-7xy' to each side of the equation. 7xy + -7xy = -5 + -7xy Combine like terms: 7xy + -7xy = 0 0 = -5 + -7xy Simplifying 0 = -5 + -7xy 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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