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