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