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