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Simplifying (3x + 2y + y2) * dx + (x + 4xy + 2x2) * dy = 0 Reorder the terms for easier multiplication: dx(3x + 2y + y2) + (x + 4xy + 2x2) * dy = 0 (3x * dx + 2y * dx + y2 * dx) + (x + 4xy + 2x2) * dy = 0 Reorder the terms: (2dxy + dxy2 + 3dx2) + (x + 4xy + 2x2) * dy = 0 (2dxy + dxy2 + 3dx2) + (x + 4xy + 2x2) * dy = 0 Reorder the terms for easier multiplication: 2dxy + dxy2 + 3dx2 + dy(x + 4xy + 2x2) = 0 2dxy + dxy2 + 3dx2 + (x * dy + 4xy * dy + 2x2 * dy) = 0 2dxy + dxy2 + 3dx2 + (dxy + 4dxy2 + 2dx2y) = 0 Reorder the terms: 2dxy + dxy + dxy2 + 4dxy2 + 3dx2 + 2dx2y = 0 Combine like terms: 2dxy + dxy = 3dxy 3dxy + dxy2 + 4dxy2 + 3dx2 + 2dx2y = 0 Combine like terms: dxy2 + 4dxy2 = 5dxy2 3dxy + 5dxy2 + 3dx2 + 2dx2y = 0 Solving 3dxy + 5dxy2 + 3dx2 + 2dx2y = 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 + 5y2 + 3x + 2xy) = 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 + 5y2 + 3x + 2xy)' equal to zero and attempt to solve: Simplifying 3y + 5y2 + 3x + 2xy = 0 Reorder the terms: 3x + 2xy + 3y + 5y2 = 0 Solving 3x + 2xy + 3y + 5y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-3x' to each side of the equation. 3x + 2xy + 3y + -3x + 5y2 = 0 + -3x Reorder the terms: 3x + -3x + 2xy + 3y + 5y2 = 0 + -3x Combine like terms: 3x + -3x = 0 0 + 2xy + 3y + 5y2 = 0 + -3x 2xy + 3y + 5y2 = 0 + -3x Remove the zero: 2xy + 3y + 5y2 = -3x Add '-2xy' to each side of the equation. 2xy + 3y + -2xy + 5y2 = -3x + -2xy Reorder the terms: 2xy + -2xy + 3y + 5y2 = -3x + -2xy Combine like terms: 2xy + -2xy = 0 0 + 3y + 5y2 = -3x + -2xy 3y + 5y2 = -3x + -2xy Add '-3y' to each side of the equation. 3y + -3y + 5y2 = -3x + -2xy + -3y Combine like terms: 3y + -3y = 0 0 + 5y2 = -3x + -2xy + -3y 5y2 = -3x + -2xy + -3y Add '-5y2' to each side of the equation. 5y2 + -5y2 = -3x + -2xy + -3y + -5y2 Combine like terms: 5y2 + -5y2 = 0 0 = -3x + -2xy + -3y + -5y2 Simplifying 0 = -3x + -2xy + -3y + -5y2 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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