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Simplifying (3xy + 6y2) * dx + (2x2 + 9xy) * dy = 0 Reorder the terms for easier multiplication: dx(3xy + 6y2) + (2x2 + 9xy) * dy = 0 (3xy * dx + 6y2 * dx) + (2x2 + 9xy) * dy = 0 Reorder the terms: (6dxy2 + 3dx2y) + (2x2 + 9xy) * dy = 0 (6dxy2 + 3dx2y) + (2x2 + 9xy) * dy = 0 Reorder the terms: 6dxy2 + 3dx2y + (9xy + 2x2) * dy = 0 Reorder the terms for easier multiplication: 6dxy2 + 3dx2y + dy(9xy + 2x2) = 0 6dxy2 + 3dx2y + (9xy * dy + 2x2 * dy) = 0 6dxy2 + 3dx2y + (9dxy2 + 2dx2y) = 0 Reorder the terms: 6dxy2 + 9dxy2 + 3dx2y + 2dx2y = 0 Combine like terms: 6dxy2 + 9dxy2 = 15dxy2 15dxy2 + 3dx2y + 2dx2y = 0 Combine like terms: 3dx2y + 2dx2y = 5dx2y 15dxy2 + 5dx2y = 0 Solving 15dxy2 + 5dx2y = 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), '5dxy'. 5dxy(3y + x) = 0 Ignore the factor 5.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 '(3y + x)' equal to zero and attempt to solve: Simplifying 3y + x = 0 Reorder the terms: x + 3y = 0 Solving x + 3y = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x + 3y = 0 + -1x Combine like terms: x + -1x = 0 0 + 3y = 0 + -1x 3y = 0 + -1x Remove the zero: 3y = -1x Add '-3y' to each side of the equation. 3y + -3y = -1x + -3y Combine like terms: 3y + -3y = 0 0 = -1x + -3y Simplifying 0 = -1x + -3y 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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