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