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Simplifying 3ydx = (3x2 + -1)(dx + -1dy) Reorder the terms: 3dxy = (-1 + 3x2)(dx + -1dy) Multiply (-1 + 3x2) * (dx + -1dy) 3dxy = (-1(dx + -1dy) + 3x2 * (dx + -1dy)) 3dxy = ((dx * -1 + -1dy * -1) + 3x2 * (dx + -1dy)) 3dxy = ((-1dx + 1dy) + 3x2 * (dx + -1dy)) 3dxy = (-1dx + 1dy + (dx * 3x2 + -1dy * 3x2)) Reorder the terms: 3dxy = (-1dx + 1dy + (-3dx2y + 3dx3)) 3dxy = (-1dx + 1dy + (-3dx2y + 3dx3)) Reorder the terms: 3dxy = (-1dx + -3dx2y + 3dx3 + 1dy) 3dxy = (-1dx + -3dx2y + 3dx3 + 1dy) Solving 3dxy = -1dx + -3dx2y + 3dx3 + 1dy Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add 'dx' to each side of the equation. dx + 3dxy = -1dx + -3dx2y + 3dx3 + dx + 1dy Reorder the terms: dx + 3dxy = -1dx + dx + -3dx2y + 3dx3 + 1dy Combine like terms: -1dx + dx = 0 dx + 3dxy = 0 + -3dx2y + 3dx3 + 1dy dx + 3dxy = -3dx2y + 3dx3 + 1dy Add '3dx2y' to each side of the equation. dx + 3dxy + 3dx2y = -3dx2y + 3dx3 + 3dx2y + 1dy Reorder the terms: dx + 3dxy + 3dx2y = -3dx2y + 3dx2y + 3dx3 + 1dy Combine like terms: -3dx2y + 3dx2y = 0 dx + 3dxy + 3dx2y = 0 + 3dx3 + 1dy dx + 3dxy + 3dx2y = 3dx3 + 1dy Add '-3dx3' to each side of the equation. dx + 3dxy + 3dx2y + -3dx3 = 3dx3 + -3dx3 + 1dy Combine like terms: 3dx3 + -3dx3 = 0 dx + 3dxy + 3dx2y + -3dx3 = 0 + 1dy dx + 3dxy + 3dx2y + -3dx3 = 1dy Add '-1dy' to each side of the equation. dx + 3dxy + 3dx2y + -3dx3 + -1dy = 1dy + -1dy Combine like terms: 1dy + -1dy = 0 dx + 3dxy + 3dx2y + -3dx3 + -1dy = 0 Factor out the Greatest Common Factor (GCF), 'd'. d(x + 3xy + 3x2y + -3x3 + -1y) = 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 '(x + 3xy + 3x2y + -3x3 + -1y)' equal to zero and attempt to solve: Simplifying x + 3xy + 3x2y + -3x3 + -1y = 0 Solving x + 3xy + 3x2y + -3x3 + -1y = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + 3xy + 3x2y + -3x3 + -1x + -1y = 0 + -1x Reorder the terms: x + -1x + 3xy + 3x2y + -3x3 + -1y = 0 + -1x Combine like terms: x + -1x = 0 0 + 3xy + 3x2y + -3x3 + -1y = 0 + -1x 3xy + 3x2y + -3x3 + -1y = 0 + -1x Remove the zero: 3xy + 3x2y + -3x3 + -1y = -1x Add '-3xy' to each side of the equation. 3xy + 3x2y + -3x3 + -3xy + -1y = -1x + -3xy Reorder the terms: 3xy + -3xy + 3x2y + -3x3 + -1y = -1x + -3xy Combine like terms: 3xy + -3xy = 0 0 + 3x2y + -3x3 + -1y = -1x + -3xy 3x2y + -3x3 + -1y = -1x + -3xy Add '-3x2y' to each side of the equation. 3x2y + -3x3 + -3x2y + -1y = -1x + -3xy + -3x2y Reorder the terms: 3x2y + -3x2y + -3x3 + -1y = -1x + -3xy + -3x2y Combine like terms: 3x2y + -3x2y = 0 0 + -3x3 + -1y = -1x + -3xy + -3x2y -3x3 + -1y = -1x + -3xy + -3x2y Add '3x3' to each side of the equation. -3x3 + 3x3 + -1y = -1x + -3xy + -3x2y + 3x3 Combine like terms: -3x3 + 3x3 = 0 0 + -1y = -1x + -3xy + -3x2y + 3x3 -1y = -1x + -3xy + -3x2y + 3x3 Add 'y' to each side of the equation. -1y + y = -1x + -3xy + -3x2y + 3x3 + y Combine like terms: -1y + y = 0 0 = -1x + -3xy + -3x2y + 3x3 + y Simplifying 0 = -1x + -3xy + -3x2y + 3x3 + y 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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