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Simplifying (2xy + 3y2) * dx + (x2 + 6xy + -3y2) * dy = 0 Reorder the terms for easier multiplication: dx(2xy + 3y2) + (x2 + 6xy + -3y2) * dy = 0 (2xy * dx + 3y2 * dx) + (x2 + 6xy + -3y2) * dy = 0 Reorder the terms: (3dxy2 + 2dx2y) + (x2 + 6xy + -3y2) * dy = 0 (3dxy2 + 2dx2y) + (x2 + 6xy + -3y2) * dy = 0 Reorder the terms: 3dxy2 + 2dx2y + (6xy + x2 + -3y2) * dy = 0 Reorder the terms for easier multiplication: 3dxy2 + 2dx2y + dy(6xy + x2 + -3y2) = 0 3dxy2 + 2dx2y + (6xy * dy + x2 * dy + -3y2 * dy) = 0 3dxy2 + 2dx2y + (6dxy2 + dx2y + -3dy3) = 0 Reorder the terms: 3dxy2 + 6dxy2 + 2dx2y + dx2y + -3dy3 = 0 Combine like terms: 3dxy2 + 6dxy2 = 9dxy2 9dxy2 + 2dx2y + dx2y + -3dy3 = 0 Combine like terms: 2dx2y + dx2y = 3dx2y 9dxy2 + 3dx2y + -3dy3 = 0 Solving 9dxy2 + 3dx2y + -3dy3 = 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), '3dy'. 3dy(3xy + x2 + -1y2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'dy' equal to zero and attempt to solve: Simplifying dy = 0 Solving dy = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dy = 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 '(3xy + x2 + -1y2)' equal to zero and attempt to solve: Simplifying 3xy + x2 + -1y2 = 0 Solving 3xy + x2 + -1y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-3xy' to each side of the equation. 3xy + x2 + -3xy + -1y2 = 0 + -3xy Reorder the terms: 3xy + -3xy + x2 + -1y2 = 0 + -3xy Combine like terms: 3xy + -3xy = 0 0 + x2 + -1y2 = 0 + -3xy x2 + -1y2 = 0 + -3xy Remove the zero: x2 + -1y2 = -3xy Add '-1x2' to each side of the equation. x2 + -1x2 + -1y2 = -3xy + -1x2 Combine like terms: x2 + -1x2 = 0 0 + -1y2 = -3xy + -1x2 -1y2 = -3xy + -1x2 Add 'y2' to each side of the equation. -1y2 + y2 = -3xy + -1x2 + y2 Combine like terms: -1y2 + y2 = 0 0 = -3xy + -1x2 + y2 Simplifying 0 = -3xy + -1x2 + y2 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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