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Simplifying (x2y + 4xy + 2y) * dx + (x2 + x) * dy = 0 Reorder the terms: (4xy + x2y + 2y) * dx + (x2 + x) * dy = 0 Reorder the terms for easier multiplication: dx(4xy + x2y + 2y) + (x2 + x) * dy = 0 (4xy * dx + x2y * dx + 2y * dx) + (x2 + x) * dy = 0 Reorder the terms: (2dxy + 4dx2y + dx3y) + (x2 + x) * dy = 0 (2dxy + 4dx2y + dx3y) + (x2 + x) * dy = 0 Reorder the terms: 2dxy + 4dx2y + dx3y + (x + x2) * dy = 0 Reorder the terms for easier multiplication: 2dxy + 4dx2y + dx3y + dy(x + x2) = 0 2dxy + 4dx2y + dx3y + (x * dy + x2 * dy) = 0 2dxy + 4dx2y + dx3y + (dxy + dx2y) = 0 Reorder the terms: 2dxy + dxy + 4dx2y + dx2y + dx3y = 0 Combine like terms: 2dxy + dxy = 3dxy 3dxy + 4dx2y + dx2y + dx3y = 0 Combine like terms: 4dx2y + dx2y = 5dx2y 3dxy + 5dx2y + dx3y = 0 Solving 3dxy + 5dx2y + 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), 'dxy'. dxy(3 + 5x + x2) = 0Subproblem 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 '(3 + 5x + x2)' equal to zero and attempt to solve: Simplifying 3 + 5x + x2 = 0 Solving 3 + 5x + x2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + 5x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 5x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 5x + x2 = 0 + -3 5x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 5x + x2 = -3 Add '-5x' to each side of the equation. 5x + -5x + x2 = -3 + -5x Combine like terms: 5x + -5x = 0 0 + x2 = -3 + -5x x2 = -3 + -5x Add '-1x2' to each side of the equation. x2 + -1x2 = -3 + -5x + -1x2 Combine like terms: x2 + -1x2 = 0 0 = -3 + -5x + -1x2 Simplifying 0 = -3 + -5x + -1x2 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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