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Simplifying (6x + -3y + 2) * dx + -1(2x + -1y + -1) * dy = 0 Reorder the terms: (2 + 6x + -3y) * dx + -1(2x + -1y + -1) * dy = 0 Reorder the terms for easier multiplication: dx(2 + 6x + -3y) + -1(2x + -1y + -1) * dy = 0 (2 * dx + 6x * dx + -3y * dx) + -1(2x + -1y + -1) * dy = 0 Reorder the terms: (2dx + -3dxy + 6dx2) + -1(2x + -1y + -1) * dy = 0 (2dx + -3dxy + 6dx2) + -1(2x + -1y + -1) * dy = 0 Reorder the terms: 2dx + -3dxy + 6dx2 + -1(-1 + 2x + -1y) * dy = 0 Reorder the terms for easier multiplication: 2dx + -3dxy + 6dx2 + -1dy(-1 + 2x + -1y) = 0 2dx + -3dxy + 6dx2 + (-1 * -1dy + 2x * -1dy + -1y * -1dy) = 0 Reorder the terms: 2dx + -3dxy + 6dx2 + (-2dxy + 1dy + 1dy2) = 0 2dx + -3dxy + 6dx2 + (-2dxy + 1dy + 1dy2) = 0 Reorder the terms: 2dx + -3dxy + -2dxy + 6dx2 + 1dy + 1dy2 = 0 Combine like terms: -3dxy + -2dxy = -5dxy 2dx + -5dxy + 6dx2 + 1dy + 1dy2 = 0 Solving 2dx + -5dxy + 6dx2 + 1dy + 1dy2 = 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 + -5xy + 6x2 + y + 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 '(2x + -5xy + 6x2 + y + y2)' equal to zero and attempt to solve: Simplifying 2x + -5xy + 6x2 + y + y2 = 0 Solving 2x + -5xy + 6x2 + y + y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-2x' to each side of the equation. 2x + -5xy + 6x2 + y + -2x + y2 = 0 + -2x Reorder the terms: 2x + -2x + -5xy + 6x2 + y + y2 = 0 + -2x Combine like terms: 2x + -2x = 0 0 + -5xy + 6x2 + y + y2 = 0 + -2x -5xy + 6x2 + y + y2 = 0 + -2x Remove the zero: -5xy + 6x2 + y + y2 = -2x Add '5xy' to each side of the equation. -5xy + 6x2 + y + 5xy + y2 = -2x + 5xy Reorder the terms: -5xy + 5xy + 6x2 + y + y2 = -2x + 5xy Combine like terms: -5xy + 5xy = 0 0 + 6x2 + y + y2 = -2x + 5xy 6x2 + y + y2 = -2x + 5xy Add '-6x2' to each side of the equation. 6x2 + y + -6x2 + y2 = -2x + 5xy + -6x2 Reorder the terms: 6x2 + -6x2 + y + y2 = -2x + 5xy + -6x2 Combine like terms: 6x2 + -6x2 = 0 0 + y + y2 = -2x + 5xy + -6x2 y + y2 = -2x + 5xy + -6x2 Add '-1y' to each side of the equation. y + -1y + y2 = -2x + 5xy + -6x2 + -1y Combine like terms: y + -1y = 0 0 + y2 = -2x + 5xy + -6x2 + -1y y2 = -2x + 5xy + -6x2 + -1y Add '-1y2' to each side of the equation. y2 + -1y2 = -2x + 5xy + -6x2 + -1y + -1y2 Combine like terms: y2 + -1y2 = 0 0 = -2x + 5xy + -6x2 + -1y + -1y2 Simplifying 0 = -2x + 5xy + -6x2 + -1y + -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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