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Simplifying (y3 + kxy4 + -2x) * dx + (3xy2 + 20x2y3) * dy = 0 Reorder the terms: (kxy4 + -2x + y3) * dx + (3xy2 + 20x2y3) * dy = 0 Reorder the terms for easier multiplication: dx(kxy4 + -2x + y3) + (3xy2 + 20x2y3) * dy = 0 (kxy4 * dx + -2x * dx + y3 * dx) + (3xy2 + 20x2y3) * dy = 0 Reorder the terms: (dkx2y4 + dxy3 + -2dx2) + (3xy2 + 20x2y3) * dy = 0 (dkx2y4 + dxy3 + -2dx2) + (3xy2 + 20x2y3) * dy = 0 Reorder the terms for easier multiplication: dkx2y4 + dxy3 + -2dx2 + dy(3xy2 + 20x2y3) = 0 dkx2y4 + dxy3 + -2dx2 + (3xy2 * dy + 20x2y3 * dy) = 0 dkx2y4 + dxy3 + -2dx2 + (3dxy3 + 20dx2y4) = 0 Reorder the terms: dkx2y4 + dxy3 + 3dxy3 + -2dx2 + 20dx2y4 = 0 Combine like terms: dxy3 + 3dxy3 = 4dxy3 dkx2y4 + 4dxy3 + -2dx2 + 20dx2y4 = 0 Solving dkx2y4 + 4dxy3 + -2dx2 + 20dx2y4 = 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(kxy4 + 4y3 + -2x + 20xy4) = 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 '(kxy4 + 4y3 + -2x + 20xy4)' equal to zero and attempt to solve: Simplifying kxy4 + 4y3 + -2x + 20xy4 = 0 Reorder the terms: kxy4 + -2x + 20xy4 + 4y3 = 0 Solving kxy4 + -2x + 20xy4 + 4y3 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1kxy4' to each side of the equation. kxy4 + -2x + 20xy4 + -1kxy4 + 4y3 = 0 + -1kxy4 Reorder the terms: kxy4 + -1kxy4 + -2x + 20xy4 + 4y3 = 0 + -1kxy4 Combine like terms: kxy4 + -1kxy4 = 0 0 + -2x + 20xy4 + 4y3 = 0 + -1kxy4 -2x + 20xy4 + 4y3 = 0 + -1kxy4 Remove the zero: -2x + 20xy4 + 4y3 = -1kxy4 Add '2x' to each side of the equation. -2x + 20xy4 + 2x + 4y3 = -1kxy4 + 2x Reorder the terms: -2x + 2x + 20xy4 + 4y3 = -1kxy4 + 2x Combine like terms: -2x + 2x = 0 0 + 20xy4 + 4y3 = -1kxy4 + 2x 20xy4 + 4y3 = -1kxy4 + 2x Add '-20xy4' to each side of the equation. 20xy4 + -20xy4 + 4y3 = -1kxy4 + 2x + -20xy4 Combine like terms: 20xy4 + -20xy4 = 0 0 + 4y3 = -1kxy4 + 2x + -20xy4 4y3 = -1kxy4 + 2x + -20xy4 Add '-4y3' to each side of the equation. 4y3 + -4y3 = -1kxy4 + 2x + -20xy4 + -4y3 Combine like terms: 4y3 + -4y3 = 0 0 = -1kxy4 + 2x + -20xy4 + -4y3 Simplifying 0 = -1kxy4 + 2x + -20xy4 + -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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