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Simplifying (3x + y + 6) * dx + (2x + y + 1) * dy = 0 Reorder the terms: (6 + 3x + y) * dx + (2x + y + 1) * dy = 0 Reorder the terms for easier multiplication: dx(6 + 3x + y) + (2x + y + 1) * dy = 0 (6 * dx + 3x * dx + y * dx) + (2x + y + 1) * dy = 0 Reorder the terms: (6dx + dxy + 3dx2) + (2x + y + 1) * dy = 0 (6dx + dxy + 3dx2) + (2x + y + 1) * dy = 0 Reorder the terms: 6dx + dxy + 3dx2 + (1 + 2x + y) * dy = 0 Reorder the terms for easier multiplication: 6dx + dxy + 3dx2 + dy(1 + 2x + y) = 0 6dx + dxy + 3dx2 + (1 * dy + 2x * dy + y * dy) = 0 Reorder the terms: 6dx + dxy + 3dx2 + (2dxy + 1dy + dy2) = 0 6dx + dxy + 3dx2 + (2dxy + 1dy + dy2) = 0 Reorder the terms: 6dx + dxy + 2dxy + 3dx2 + 1dy + dy2 = 0 Combine like terms: dxy + 2dxy = 3dxy 6dx + 3dxy + 3dx2 + 1dy + dy2 = 0 Solving 6dx + 3dxy + 3dx2 + 1dy + dy2 = 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(6x + 3xy + 3x2 + y + y2) = 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 '(6x + 3xy + 3x2 + y + y2)' equal to zero and attempt to solve: Simplifying 6x + 3xy + 3x2 + y + y2 = 0 Solving 6x + 3xy + 3x2 + y + y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-6x' to each side of the equation. 6x + 3xy + 3x2 + y + -6x + y2 = 0 + -6x Reorder the terms: 6x + -6x + 3xy + 3x2 + y + y2 = 0 + -6x Combine like terms: 6x + -6x = 0 0 + 3xy + 3x2 + y + y2 = 0 + -6x 3xy + 3x2 + y + y2 = 0 + -6x Remove the zero: 3xy + 3x2 + y + y2 = -6x Add '-3xy' to each side of the equation. 3xy + 3x2 + y + -3xy + y2 = -6x + -3xy Reorder the terms: 3xy + -3xy + 3x2 + y + y2 = -6x + -3xy Combine like terms: 3xy + -3xy = 0 0 + 3x2 + y + y2 = -6x + -3xy 3x2 + y + y2 = -6x + -3xy Add '-3x2' to each side of the equation. 3x2 + y + -3x2 + y2 = -6x + -3xy + -3x2 Reorder the terms: 3x2 + -3x2 + y + y2 = -6x + -3xy + -3x2 Combine like terms: 3x2 + -3x2 = 0 0 + y + y2 = -6x + -3xy + -3x2 y + y2 = -6x + -3xy + -3x2 Add '-1y' to each side of the equation. y + -1y + y2 = -6x + -3xy + -3x2 + -1y Combine like terms: y + -1y = 0 0 + y2 = -6x + -3xy + -3x2 + -1y y2 = -6x + -3xy + -3x2 + -1y Add '-1y2' to each side of the equation. y2 + -1y2 = -6x + -3xy + -3x2 + -1y + -1y2 Combine like terms: y2 + -1y2 = 0 0 = -6x + -3xy + -3x2 + -1y + -1y2 Simplifying 0 = -6x + -3xy + -3x2 + -1y + -1y2 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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