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Simplifying (x2 + y2) * dx + (x3 + 3xy2 + 2xy) * dy = 0 Reorder the terms for easier multiplication: dx(x2 + y2) + (x3 + 3xy2 + 2xy) * dy = 0 (x2 * dx + y2 * dx) + (x3 + 3xy2 + 2xy) * dy = 0 Reorder the terms: (dxy2 + dx3) + (x3 + 3xy2 + 2xy) * dy = 0 (dxy2 + dx3) + (x3 + 3xy2 + 2xy) * dy = 0 Reorder the terms: dxy2 + dx3 + (2xy + 3xy2 + x3) * dy = 0 Reorder the terms for easier multiplication: dxy2 + dx3 + dy(2xy + 3xy2 + x3) = 0 dxy2 + dx3 + (2xy * dy + 3xy2 * dy + x3 * dy) = 0 dxy2 + dx3 + (2dxy2 + 3dxy3 + dx3y) = 0 Reorder the terms: dxy2 + 2dxy2 + 3dxy3 + dx3 + dx3y = 0 Combine like terms: dxy2 + 2dxy2 = 3dxy2 3dxy2 + 3dxy3 + dx3 + dx3y = 0 Solving 3dxy2 + 3dxy3 + dx3 + dx3y = 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), 'dx'. dx(3y2 + 3y3 + x2 + x2y) = 0Subproblem 1
Set the factor 'dx' equal to zero and attempt to solve: Simplifying dx = 0 Solving dx = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dx = 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 '(3y2 + 3y3 + x2 + x2y)' equal to zero and attempt to solve: Simplifying 3y2 + 3y3 + x2 + x2y = 0 Reorder the terms: x2 + x2y + 3y2 + 3y3 = 0 Solving x2 + x2y + 3y2 + 3y3 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x2' to each side of the equation. x2 + x2y + 3y2 + -1x2 + 3y3 = 0 + -1x2 Reorder the terms: x2 + -1x2 + x2y + 3y2 + 3y3 = 0 + -1x2 Combine like terms: x2 + -1x2 = 0 0 + x2y + 3y2 + 3y3 = 0 + -1x2 x2y + 3y2 + 3y3 = 0 + -1x2 Remove the zero: x2y + 3y2 + 3y3 = -1x2 Add '-1x2y' to each side of the equation. x2y + 3y2 + -1x2y + 3y3 = -1x2 + -1x2y Reorder the terms: x2y + -1x2y + 3y2 + 3y3 = -1x2 + -1x2y Combine like terms: x2y + -1x2y = 0 0 + 3y2 + 3y3 = -1x2 + -1x2y 3y2 + 3y3 = -1x2 + -1x2y Add '-3y2' to each side of the equation. 3y2 + -3y2 + 3y3 = -1x2 + -1x2y + -3y2 Combine like terms: 3y2 + -3y2 = 0 0 + 3y3 = -1x2 + -1x2y + -3y2 3y3 = -1x2 + -1x2y + -3y2 Add '-3y3' to each side of the equation. 3y3 + -3y3 = -1x2 + -1x2y + -3y2 + -3y3 Combine like terms: 3y3 + -3y3 = 0 0 = -1x2 + -1x2y + -3y2 + -3y3 Simplifying 0 = -1x2 + -1x2y + -3y2 + -3y3 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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