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Simplifying (3x2y + y2) * dx + (3x3 + -1y2 + 4xy) * dy = 0 Reorder the terms for easier multiplication: dx(3x2y + y2) + (3x3 + -1y2 + 4xy) * dy = 0 (3x2y * dx + y2 * dx) + (3x3 + -1y2 + 4xy) * dy = 0 Reorder the terms: (dxy2 + 3dx3y) + (3x3 + -1y2 + 4xy) * dy = 0 (dxy2 + 3dx3y) + (3x3 + -1y2 + 4xy) * dy = 0 Reorder the terms: dxy2 + 3dx3y + (4xy + 3x3 + -1y2) * dy = 0 Reorder the terms for easier multiplication: dxy2 + 3dx3y + dy(4xy + 3x3 + -1y2) = 0 dxy2 + 3dx3y + (4xy * dy + 3x3 * dy + -1y2 * dy) = 0 dxy2 + 3dx3y + (4dxy2 + 3dx3y + -1dy3) = 0 Reorder the terms: dxy2 + 4dxy2 + 3dx3y + 3dx3y + -1dy3 = 0 Combine like terms: dxy2 + 4dxy2 = 5dxy2 5dxy2 + 3dx3y + 3dx3y + -1dy3 = 0 Combine like terms: 3dx3y + 3dx3y = 6dx3y 5dxy2 + 6dx3y + -1dy3 = 0 Solving 5dxy2 + 6dx3y + -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(5xy + 6x3 + -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 '(5xy + 6x3 + -1y2)' equal to zero and attempt to solve: Simplifying 5xy + 6x3 + -1y2 = 0 Solving 5xy + 6x3 + -1y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-5xy' to each side of the equation. 5xy + 6x3 + -5xy + -1y2 = 0 + -5xy Reorder the terms: 5xy + -5xy + 6x3 + -1y2 = 0 + -5xy Combine like terms: 5xy + -5xy = 0 0 + 6x3 + -1y2 = 0 + -5xy 6x3 + -1y2 = 0 + -5xy Remove the zero: 6x3 + -1y2 = -5xy Add '-6x3' to each side of the equation. 6x3 + -6x3 + -1y2 = -5xy + -6x3 Combine like terms: 6x3 + -6x3 = 0 0 + -1y2 = -5xy + -6x3 -1y2 = -5xy + -6x3 Add 'y2' to each side of the equation. -1y2 + y2 = -5xy + -6x3 + y2 Combine like terms: -1y2 + y2 = 0 0 = -5xy + -6x3 + y2 Simplifying 0 = -5xy + -6x3 + 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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