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Simplifying (4y3 + -14x2y + 8y2x) * dx + (-8x2y + 2y2x + 12x3) * dy = 0 Reorder the terms: (8xy2 + -14x2y + 4y3) * dx + (-8x2y + 2y2x + 12x3) * dy = 0 Reorder the terms for easier multiplication: dx(8xy2 + -14x2y + 4y3) + (-8x2y + 2y2x + 12x3) * dy = 0 (8xy2 * dx + -14x2y * dx + 4y3 * dx) + (-8x2y + 2y2x + 12x3) * dy = 0 Reorder the terms: (4dxy3 + 8dx2y2 + -14dx3y) + (-8x2y + 2y2x + 12x3) * dy = 0 (4dxy3 + 8dx2y2 + -14dx3y) + (-8x2y + 2y2x + 12x3) * dy = 0 Reorder the terms: 4dxy3 + 8dx2y2 + -14dx3y + (2xy2 + -8x2y + 12x3) * dy = 0 Reorder the terms for easier multiplication: 4dxy3 + 8dx2y2 + -14dx3y + dy(2xy2 + -8x2y + 12x3) = 0 4dxy3 + 8dx2y2 + -14dx3y + (2xy2 * dy + -8x2y * dy + 12x3 * dy) = 0 4dxy3 + 8dx2y2 + -14dx3y + (2dxy3 + -8dx2y2 + 12dx3y) = 0 Reorder the terms: 4dxy3 + 2dxy3 + 8dx2y2 + -8dx2y2 + -14dx3y + 12dx3y = 0 Combine like terms: 4dxy3 + 2dxy3 = 6dxy3 6dxy3 + 8dx2y2 + -8dx2y2 + -14dx3y + 12dx3y = 0 Combine like terms: 8dx2y2 + -8dx2y2 = 0 6dxy3 + 0 + -14dx3y + 12dx3y = 0 6dxy3 + -14dx3y + 12dx3y = 0 Combine like terms: -14dx3y + 12dx3y = -2dx3y 6dxy3 + -2dx3y = 0 Solving 6dxy3 + -2dx3y = 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(3y2 + -1x2) = 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 '(3y2 + -1x2)' equal to zero and attempt to solve: Simplifying 3y2 + -1x2 = 0 Reorder the terms: -1x2 + 3y2 = 0 Solving -1x2 + 3y2 = 0 Move all terms containing d to the left, all other terms to the right. Add 'x2' to each side of the equation. -1x2 + x2 + 3y2 = 0 + x2 Combine like terms: -1x2 + x2 = 0 0 + 3y2 = 0 + x2 3y2 = 0 + x2 Remove the zero: 3y2 = x2 Add '-3y2' to each side of the equation. 3y2 + -3y2 = x2 + -3y2 Combine like terms: 3y2 + -3y2 = 0 0 = x2 + -3y2 Simplifying 0 = x2 + -3y2 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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