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Simplifying X(3xy + -4y + 6) * dx + (x + -6xy + -1) * dy = 0 Reorder the terms: X(6 + 3xy + -4y) * dx + (x + -6xy + -1) * dy = 0 Reorder the terms for easier multiplication: X * dx(6 + 3xy + -4y) + (x + -6xy + -1) * dy = 0 Multiply X * dx dxX(6 + 3xy + -4y) + (x + -6xy + -1) * dy = 0 (6 * dxX + 3xy * dxX + -4y * dxX) + (x + -6xy + -1) * dy = 0 Reorder the terms: (6dxX + -4dxyX + 3dx2yX) + (x + -6xy + -1) * dy = 0 (6dxX + -4dxyX + 3dx2yX) + (x + -6xy + -1) * dy = 0 Reorder the terms: 6dxX + -4dxyX + 3dx2yX + (-1 + x + -6xy) * dy = 0 Reorder the terms for easier multiplication: 6dxX + -4dxyX + 3dx2yX + dy(-1 + x + -6xy) = 0 6dxX + -4dxyX + 3dx2yX + (-1 * dy + x * dy + -6xy * dy) = 0 Reorder the terms: 6dxX + -4dxyX + 3dx2yX + (dxy + -6dxy2 + -1dy) = 0 6dxX + -4dxyX + 3dx2yX + (dxy + -6dxy2 + -1dy) = 0 Reorder the terms: 6dxX + dxy + -4dxyX + -6dxy2 + 3dx2yX + -1dy = 0 Solving 6dxX + dxy + -4dxyX + -6dxy2 + 3dx2yX + -1dy = 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), 'd'. d(6xX + xy + -4xyX + -6xy2 + 3x2yX + -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 '(6xX + xy + -4xyX + -6xy2 + 3x2yX + -1y)' equal to zero and attempt to solve: Simplifying 6xX + xy + -4xyX + -6xy2 + 3x2yX + -1y = 0 Solving 6xX + xy + -4xyX + -6xy2 + 3x2yX + -1y = 0 Move all terms containing d to the left, all other terms to the right. Add '-6xX' to each side of the equation. 6xX + xy + -4xyX + -6xy2 + 3x2yX + -6xX + -1y = 0 + -6xX Reorder the terms: 6xX + -6xX + xy + -4xyX + -6xy2 + 3x2yX + -1y = 0 + -6xX Combine like terms: 6xX + -6xX = 0 0 + xy + -4xyX + -6xy2 + 3x2yX + -1y = 0 + -6xX xy + -4xyX + -6xy2 + 3x2yX + -1y = 0 + -6xX Remove the zero: xy + -4xyX + -6xy2 + 3x2yX + -1y = -6xX Add '-1xy' to each side of the equation. xy + -4xyX + -6xy2 + 3x2yX + -1xy + -1y = -6xX + -1xy Reorder the terms: xy + -1xy + -4xyX + -6xy2 + 3x2yX + -1y = -6xX + -1xy Combine like terms: xy + -1xy = 0 0 + -4xyX + -6xy2 + 3x2yX + -1y = -6xX + -1xy -4xyX + -6xy2 + 3x2yX + -1y = -6xX + -1xy Add '4xyX' to each side of the equation. -4xyX + -6xy2 + 3x2yX + 4xyX + -1y = -6xX + -1xy + 4xyX Reorder the terms: -4xyX + 4xyX + -6xy2 + 3x2yX + -1y = -6xX + -1xy + 4xyX Combine like terms: -4xyX + 4xyX = 0 0 + -6xy2 + 3x2yX + -1y = -6xX + -1xy + 4xyX -6xy2 + 3x2yX + -1y = -6xX + -1xy + 4xyX Add '6xy2' to each side of the equation. -6xy2 + 3x2yX + 6xy2 + -1y = -6xX + -1xy + 4xyX + 6xy2 Reorder the terms: -6xy2 + 6xy2 + 3x2yX + -1y = -6xX + -1xy + 4xyX + 6xy2 Combine like terms: -6xy2 + 6xy2 = 0 0 + 3x2yX + -1y = -6xX + -1xy + 4xyX + 6xy2 3x2yX + -1y = -6xX + -1xy + 4xyX + 6xy2 Add '-3x2yX' to each side of the equation. 3x2yX + -3x2yX + -1y = -6xX + -1xy + 4xyX + 6xy2 + -3x2yX Combine like terms: 3x2yX + -3x2yX = 0 0 + -1y = -6xX + -1xy + 4xyX + 6xy2 + -3x2yX -1y = -6xX + -1xy + 4xyX + 6xy2 + -3x2yX Add 'y' to each side of the equation. -1y + y = -6xX + -1xy + 4xyX + 6xy2 + -3x2yX + y Combine like terms: -1y + y = 0 0 = -6xX + -1xy + 4xyX + 6xy2 + -3x2yX + y Simplifying 0 = -6xX + -1xy + 4xyX + 6xy2 + -3x2yX + 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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