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