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Simplifying (6x2y2 + 4y4) * dx + (2x3 + 4xy3) * dy = 0 Reorder the terms for easier multiplication: dx(6x2y2 + 4y4) + (2x3 + 4xy3) * dy = 0 (6x2y2 * dx + 4y4 * dx) + (2x3 + 4xy3) * dy = 0 Reorder the terms: (4dxy4 + 6dx3y2) + (2x3 + 4xy3) * dy = 0 (4dxy4 + 6dx3y2) + (2x3 + 4xy3) * dy = 0 Reorder the terms: 4dxy4 + 6dx3y2 + (4xy3 + 2x3) * dy = 0 Reorder the terms for easier multiplication: 4dxy4 + 6dx3y2 + dy(4xy3 + 2x3) = 0 4dxy4 + 6dx3y2 + (4xy3 * dy + 2x3 * dy) = 0 4dxy4 + 6dx3y2 + (4dxy4 + 2dx3y) = 0 Reorder the terms: 4dxy4 + 4dxy4 + 2dx3y + 6dx3y2 = 0 Combine like terms: 4dxy4 + 4dxy4 = 8dxy4 8dxy4 + 2dx3y + 6dx3y2 = 0 Solving 8dxy4 + 2dx3y + 6dx3y2 = 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(4y3 + x2 + 3x2y) = 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 '(4y3 + x2 + 3x2y)' equal to zero and attempt to solve: Simplifying 4y3 + x2 + 3x2y = 0 Reorder the terms: x2 + 3x2y + 4y3 = 0 Solving x2 + 3x2y + 4y3 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x2' to each side of the equation. x2 + 3x2y + -1x2 + 4y3 = 0 + -1x2 Reorder the terms: x2 + -1x2 + 3x2y + 4y3 = 0 + -1x2 Combine like terms: x2 + -1x2 = 0 0 + 3x2y + 4y3 = 0 + -1x2 3x2y + 4y3 = 0 + -1x2 Remove the zero: 3x2y + 4y3 = -1x2 Add '-3x2y' to each side of the equation. 3x2y + -3x2y + 4y3 = -1x2 + -3x2y Combine like terms: 3x2y + -3x2y = 0 0 + 4y3 = -1x2 + -3x2y 4y3 = -1x2 + -3x2y Add '-4y3' to each side of the equation. 4y3 + -4y3 = -1x2 + -3x2y + -4y3 Combine like terms: 4y3 + -4y3 = 0 0 = -1x2 + -3x2y + -4y3 Simplifying 0 = -1x2 + -3x2y + -4y3 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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