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Simplifying (x3 + 3x + 1) * dy = (2y + 1) * dx Reorder the terms: (1 + 3x + x3) * dy = (2y + 1) * dx Reorder the terms for easier multiplication: dy(1 + 3x + x3) = (2y + 1) * dx (1 * dy + 3x * dy + x3 * dy) = (2y + 1) * dx Reorder the terms: (3dxy + dx3y + 1dy) = (2y + 1) * dx (3dxy + dx3y + 1dy) = (2y + 1) * dx Reorder the terms: 3dxy + dx3y + 1dy = (1 + 2y) * dx Reorder the terms for easier multiplication: 3dxy + dx3y + 1dy = dx(1 + 2y) 3dxy + dx3y + 1dy = (1 * dx + 2y * dx) 3dxy + dx3y + 1dy = (1dx + 2dxy) Solving 3dxy + dx3y + 1dy = 1dx + 2dxy Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1dx' to each side of the equation. 3dxy + dx3y + -1dx + 1dy = 1dx + -1dx + 2dxy Reorder the terms: -1dx + 3dxy + dx3y + 1dy = 1dx + -1dx + 2dxy Combine like terms: 1dx + -1dx = 0 -1dx + 3dxy + dx3y + 1dy = 0 + 2dxy -1dx + 3dxy + dx3y + 1dy = 2dxy Add '-2dxy' to each side of the equation. -1dx + 3dxy + dx3y + -2dxy + 1dy = 2dxy + -2dxy Reorder the terms: -1dx + 3dxy + -2dxy + dx3y + 1dy = 2dxy + -2dxy Combine like terms: 3dxy + -2dxy = 1dxy -1dx + 1dxy + dx3y + 1dy = 2dxy + -2dxy Combine like terms: 2dxy + -2dxy = 0 -1dx + 1dxy + dx3y + 1dy = 0 Factor out the Greatest Common Factor (GCF), 'd'. d(-1x + xy + x3y + y) = 0Subproblem 1
Set the factor 'd' equal to zero and attempt to solve: Simplifying d = 0 Solving d = 0 Move all terms containing d to the left, all other terms to the right. Simplifying d = 0Subproblem 2
Set the factor '(-1x + xy + x3y + y)' equal to zero and attempt to solve: Simplifying -1x + xy + x3y + y = 0 Solving -1x + xy + x3y + y = 0 Move all terms containing d to the left, all other terms to the right. Add 'x' to each side of the equation. -1x + xy + x3y + x + y = 0 + x Reorder the terms: -1x + x + xy + x3y + y = 0 + x Combine like terms: -1x + x = 0 0 + xy + x3y + y = 0 + x xy + x3y + y = 0 + x Remove the zero: xy + x3y + y = x Add '-1xy' to each side of the equation. xy + x3y + -1xy + y = x + -1xy Reorder the terms: xy + -1xy + x3y + y = x + -1xy Combine like terms: xy + -1xy = 0 0 + x3y + y = x + -1xy x3y + y = x + -1xy Add '-1x3y' to each side of the equation. x3y + -1x3y + y = x + -1xy + -1x3y Combine like terms: x3y + -1x3y = 0 0 + y = x + -1xy + -1x3y y = x + -1xy + -1x3y Add '-1y' to each side of the equation. y + -1y = x + -1xy + -1x3y + -1y Combine like terms: y + -1y = 0 0 = x + -1xy + -1x3y + -1y Simplifying 0 = x + -1xy + -1x3y + -1y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
d = {0}
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