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Simplifying 2y(x2 + -1x + -1) * dx + (x3 + x) * dy = 0 Reorder the terms: 2y(-1 + -1x + x2) * dx + (x3 + x) * dy = 0 Reorder the terms for easier multiplication: 2y * dx(-1 + -1x + x2) + (x3 + x) * dy = 0 Multiply y * dx 2dxy(-1 + -1x + x2) + (x3 + x) * dy = 0 (-1 * 2dxy + -1x * 2dxy + x2 * 2dxy) + (x3 + x) * dy = 0 (-2dxy + -2dx2y + 2dx3y) + (x3 + x) * dy = 0 Reorder the terms: -2dxy + -2dx2y + 2dx3y + (x + x3) * dy = 0 Reorder the terms for easier multiplication: -2dxy + -2dx2y + 2dx3y + dy(x + x3) = 0 -2dxy + -2dx2y + 2dx3y + (x * dy + x3 * dy) = 0 -2dxy + -2dx2y + 2dx3y + (dxy + dx3y) = 0 Reorder the terms: -2dxy + dxy + -2dx2y + 2dx3y + dx3y = 0 Combine like terms: -2dxy + dxy = -1dxy -1dxy + -2dx2y + 2dx3y + dx3y = 0 Combine like terms: 2dx3y + dx3y = 3dx3y -1dxy + -2dx2y + 3dx3y = 0 Solving -1dxy + -2dx2y + 3dx3y = 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(-1 + -2x + 3x2) = 0 Factor a trinomial. dxy((-1 + -3x)(1 + -1x)) = 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 '(-1 + -3x)' equal to zero and attempt to solve: Simplifying -1 + -3x = 0 Solving -1 + -3x = 0 Move all terms containing d to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -3x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3x = 0 + 1 -3x = 0 + 1 Combine like terms: 0 + 1 = 1 -3x = 1 Add '3x' to each side of the equation. -3x + 3x = 1 + 3x Combine like terms: -3x + 3x = 0 0 = 1 + 3x Simplifying 0 = 1 + 3x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing d to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Add 'x' to each side of the equation. -1x + x = -1 + x Combine like terms: -1x + x = 0 0 = -1 + x Simplifying 0 = -1 + x 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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