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Simplifying (y2 + 3xy) * dx + (x2 + xy) * dy = 0 Reorder the terms: (3xy + y2) * dx + (x2 + xy) * dy = 0 Reorder the terms for easier multiplication: dx(3xy + y2) + (x2 + xy) * dy = 0 (3xy * dx + y2 * dx) + (x2 + xy) * dy = 0 Reorder the terms: (dxy2 + 3dx2y) + (x2 + xy) * dy = 0 (dxy2 + 3dx2y) + (x2 + xy) * dy = 0 Reorder the terms: dxy2 + 3dx2y + (xy + x2) * dy = 0 Reorder the terms for easier multiplication: dxy2 + 3dx2y + dy(xy + x2) = 0 dxy2 + 3dx2y + (xy * dy + x2 * dy) = 0 dxy2 + 3dx2y + (dxy2 + dx2y) = 0 Reorder the terms: dxy2 + dxy2 + 3dx2y + dx2y = 0 Combine like terms: dxy2 + dxy2 = 2dxy2 2dxy2 + 3dx2y + dx2y = 0 Combine like terms: 3dx2y + dx2y = 4dx2y 2dxy2 + 4dx2y = 0 Solving 2dxy2 + 4dx2y = 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), '2dxy'. 2dxy(y + 2x) = 0 Ignore the factor 2.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 '(y + 2x)' equal to zero and attempt to solve: Simplifying y + 2x = 0 Reorder the terms: 2x + y = 0 Solving 2x + y = 0 Move all terms containing d to the left, all other terms to the right. Add '-2x' to each side of the equation. 2x + -2x + y = 0 + -2x Combine like terms: 2x + -2x = 0 0 + y = 0 + -2x y = 0 + -2x Remove the zero: y = -2x Add '-1y' to each side of the equation. y + -1y = -2x + -1y Combine like terms: y + -1y = 0 0 = -2x + -1y Simplifying 0 = -2x + -1y 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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