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Simplifying (2xy + 3y2) * dx + (2xy + y2) * dy = 0 Reorder the terms for easier multiplication: dx(2xy + 3y2) + (2xy + y2) * dy = 0 (2xy * dx + 3y2 * dx) + (2xy + y2) * dy = 0 Reorder the terms: (3dxy2 + 2dx2y) + (2xy + y2) * dy = 0 (3dxy2 + 2dx2y) + (2xy + y2) * dy = 0 Reorder the terms for easier multiplication: 3dxy2 + 2dx2y + dy(2xy + y2) = 0 3dxy2 + 2dx2y + (2xy * dy + y2 * dy) = 0 3dxy2 + 2dx2y + (2dxy2 + dy3) = 0 Reorder the terms: 3dxy2 + 2dxy2 + 2dx2y + dy3 = 0 Combine like terms: 3dxy2 + 2dxy2 = 5dxy2 5dxy2 + 2dx2y + dy3 = 0 Solving 5dxy2 + 2dx2y + dy3 = 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(5xy + 2x2 + y2) = 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 '(5xy + 2x2 + y2)' equal to zero and attempt to solve: Simplifying 5xy + 2x2 + y2 = 0 Solving 5xy + 2x2 + y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-5xy' to each side of the equation. 5xy + 2x2 + -5xy + y2 = 0 + -5xy Reorder the terms: 5xy + -5xy + 2x2 + y2 = 0 + -5xy Combine like terms: 5xy + -5xy = 0 0 + 2x2 + y2 = 0 + -5xy 2x2 + y2 = 0 + -5xy Remove the zero: 2x2 + y2 = -5xy Add '-2x2' to each side of the equation. 2x2 + -2x2 + y2 = -5xy + -2x2 Combine like terms: 2x2 + -2x2 = 0 0 + y2 = -5xy + -2x2 y2 = -5xy + -2x2 Add '-1y2' to each side of the equation. y2 + -1y2 = -5xy + -2x2 + -1y2 Combine like terms: y2 + -1y2 = 0 0 = -5xy + -2x2 + -1y2 Simplifying 0 = -5xy + -2x2 + -1y2 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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