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Simplifying (x + 2y + 2) * dx + (-3x + -6y + 4) * dy = 0 Reorder the terms: (2 + x + 2y) * dx + (-3x + -6y + 4) * dy = 0 Reorder the terms for easier multiplication: dx(2 + x + 2y) + (-3x + -6y + 4) * dy = 0 (2 * dx + x * dx + 2y * dx) + (-3x + -6y + 4) * dy = 0 Reorder the terms: (2dx + 2dxy + dx2) + (-3x + -6y + 4) * dy = 0 (2dx + 2dxy + dx2) + (-3x + -6y + 4) * dy = 0 Reorder the terms: 2dx + 2dxy + dx2 + (4 + -3x + -6y) * dy = 0 Reorder the terms for easier multiplication: 2dx + 2dxy + dx2 + dy(4 + -3x + -6y) = 0 2dx + 2dxy + dx2 + (4 * dy + -3x * dy + -6y * dy) = 0 Reorder the terms: 2dx + 2dxy + dx2 + (-3dxy + 4dy + -6dy2) = 0 2dx + 2dxy + dx2 + (-3dxy + 4dy + -6dy2) = 0 Reorder the terms: 2dx + 2dxy + -3dxy + dx2 + 4dy + -6dy2 = 0 Combine like terms: 2dxy + -3dxy = -1dxy 2dx + -1dxy + dx2 + 4dy + -6dy2 = 0 Solving 2dx + -1dxy + dx2 + 4dy + -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(2x + -1xy + x2 + 4y + -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 '(2x + -1xy + x2 + 4y + -6y2)' equal to zero and attempt to solve: Simplifying 2x + -1xy + x2 + 4y + -6y2 = 0 Solving 2x + -1xy + x2 + 4y + -6y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-2x' to each side of the equation. 2x + -1xy + x2 + 4y + -2x + -6y2 = 0 + -2x Reorder the terms: 2x + -2x + -1xy + x2 + 4y + -6y2 = 0 + -2x Combine like terms: 2x + -2x = 0 0 + -1xy + x2 + 4y + -6y2 = 0 + -2x -1xy + x2 + 4y + -6y2 = 0 + -2x Remove the zero: -1xy + x2 + 4y + -6y2 = -2x Add 'xy' to each side of the equation. -1xy + x2 + 4y + xy + -6y2 = -2x + xy Reorder the terms: -1xy + xy + x2 + 4y + -6y2 = -2x + xy Combine like terms: -1xy + xy = 0 0 + x2 + 4y + -6y2 = -2x + xy x2 + 4y + -6y2 = -2x + xy Add '-1x2' to each side of the equation. x2 + 4y + -1x2 + -6y2 = -2x + xy + -1x2 Reorder the terms: x2 + -1x2 + 4y + -6y2 = -2x + xy + -1x2 Combine like terms: x2 + -1x2 = 0 0 + 4y + -6y2 = -2x + xy + -1x2 4y + -6y2 = -2x + xy + -1x2 Add '-4y' to each side of the equation. 4y + -4y + -6y2 = -2x + xy + -1x2 + -4y Combine like terms: 4y + -4y = 0 0 + -6y2 = -2x + xy + -1x2 + -4y -6y2 = -2x + xy + -1x2 + -4y Add '6y2' to each side of the equation. -6y2 + 6y2 = -2x + xy + -1x2 + -4y + 6y2 Combine like terms: -6y2 + 6y2 = 0 0 = -2x + xy + -1x2 + -4y + 6y2 Simplifying 0 = -2x + xy + -1x2 + -4y + 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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