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Simplifying (3x2 + 6xy + 3y) * dx + (2x2 + 3xy) * dy = 0 Reorder the terms: (6xy + 3x2 + 3y) * dx + (2x2 + 3xy) * dy = 0 Reorder the terms for easier multiplication: dx(6xy + 3x2 + 3y) + (2x2 + 3xy) * dy = 0 (6xy * dx + 3x2 * dx + 3y * dx) + (2x2 + 3xy) * dy = 0 Reorder the terms: (3dxy + 6dx2y + 3dx3) + (2x2 + 3xy) * dy = 0 (3dxy + 6dx2y + 3dx3) + (2x2 + 3xy) * dy = 0 Reorder the terms: 3dxy + 6dx2y + 3dx3 + (3xy + 2x2) * dy = 0 Reorder the terms for easier multiplication: 3dxy + 6dx2y + 3dx3 + dy(3xy + 2x2) = 0 3dxy + 6dx2y + 3dx3 + (3xy * dy + 2x2 * dy) = 0 3dxy + 6dx2y + 3dx3 + (3dxy2 + 2dx2y) = 0 Reorder the terms: 3dxy + 3dxy2 + 6dx2y + 2dx2y + 3dx3 = 0 Combine like terms: 6dx2y + 2dx2y = 8dx2y 3dxy + 3dxy2 + 8dx2y + 3dx3 = 0 Solving 3dxy + 3dxy2 + 8dx2y + 3dx3 = 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), 'dx'. dx(3y + 3y2 + 8xy + 3x2) = 0Subproblem 1
Set the factor 'dx' equal to zero and attempt to solve: Simplifying dx = 0 Solving dx = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dx = 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 '(3y + 3y2 + 8xy + 3x2)' equal to zero and attempt to solve: Simplifying 3y + 3y2 + 8xy + 3x2 = 0 Reorder the terms: 8xy + 3x2 + 3y + 3y2 = 0 Solving 8xy + 3x2 + 3y + 3y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-8xy' to each side of the equation. 8xy + 3x2 + 3y + -8xy + 3y2 = 0 + -8xy Reorder the terms: 8xy + -8xy + 3x2 + 3y + 3y2 = 0 + -8xy Combine like terms: 8xy + -8xy = 0 0 + 3x2 + 3y + 3y2 = 0 + -8xy 3x2 + 3y + 3y2 = 0 + -8xy Remove the zero: 3x2 + 3y + 3y2 = -8xy Add '-3x2' to each side of the equation. 3x2 + 3y + -3x2 + 3y2 = -8xy + -3x2 Reorder the terms: 3x2 + -3x2 + 3y + 3y2 = -8xy + -3x2 Combine like terms: 3x2 + -3x2 = 0 0 + 3y + 3y2 = -8xy + -3x2 3y + 3y2 = -8xy + -3x2 Add '-3y' to each side of the equation. 3y + -3y + 3y2 = -8xy + -3x2 + -3y Combine like terms: 3y + -3y = 0 0 + 3y2 = -8xy + -3x2 + -3y 3y2 = -8xy + -3x2 + -3y Add '-3y2' to each side of the equation. 3y2 + -3y2 = -8xy + -3x2 + -3y + -3y2 Combine like terms: 3y2 + -3y2 = 0 0 = -8xy + -3x2 + -3y + -3y2 Simplifying 0 = -8xy + -3x2 + -3y + -3y2 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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