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Simplifying (2x + 3y + 2) * dx + (6x + 9y + -2) * dy = 0 Reorder the terms: (2 + 2x + 3y) * dx + (6x + 9y + -2) * dy = 0 Reorder the terms for easier multiplication: dx(2 + 2x + 3y) + (6x + 9y + -2) * dy = 0 (2 * dx + 2x * dx + 3y * dx) + (6x + 9y + -2) * dy = 0 Reorder the terms: (2dx + 3dxy + 2dx2) + (6x + 9y + -2) * dy = 0 (2dx + 3dxy + 2dx2) + (6x + 9y + -2) * dy = 0 Reorder the terms: 2dx + 3dxy + 2dx2 + (-2 + 6x + 9y) * dy = 0 Reorder the terms for easier multiplication: 2dx + 3dxy + 2dx2 + dy(-2 + 6x + 9y) = 0 2dx + 3dxy + 2dx2 + (-2 * dy + 6x * dy + 9y * dy) = 0 Reorder the terms: 2dx + 3dxy + 2dx2 + (6dxy + -2dy + 9dy2) = 0 2dx + 3dxy + 2dx2 + (6dxy + -2dy + 9dy2) = 0 Reorder the terms: 2dx + 3dxy + 6dxy + 2dx2 + -2dy + 9dy2 = 0 Combine like terms: 3dxy + 6dxy = 9dxy 2dx + 9dxy + 2dx2 + -2dy + 9dy2 = 0 Solving 2dx + 9dxy + 2dx2 + -2dy + 9dy2 = 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 + 9xy + 2x2 + -2y + 9y2) = 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 + 9xy + 2x2 + -2y + 9y2)' equal to zero and attempt to solve: Simplifying 2x + 9xy + 2x2 + -2y + 9y2 = 0 Solving 2x + 9xy + 2x2 + -2y + 9y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-2x' to each side of the equation. 2x + 9xy + 2x2 + -2y + -2x + 9y2 = 0 + -2x Reorder the terms: 2x + -2x + 9xy + 2x2 + -2y + 9y2 = 0 + -2x Combine like terms: 2x + -2x = 0 0 + 9xy + 2x2 + -2y + 9y2 = 0 + -2x 9xy + 2x2 + -2y + 9y2 = 0 + -2x Remove the zero: 9xy + 2x2 + -2y + 9y2 = -2x Add '-9xy' to each side of the equation. 9xy + 2x2 + -2y + -9xy + 9y2 = -2x + -9xy Reorder the terms: 9xy + -9xy + 2x2 + -2y + 9y2 = -2x + -9xy Combine like terms: 9xy + -9xy = 0 0 + 2x2 + -2y + 9y2 = -2x + -9xy 2x2 + -2y + 9y2 = -2x + -9xy Add '-2x2' to each side of the equation. 2x2 + -2y + -2x2 + 9y2 = -2x + -9xy + -2x2 Reorder the terms: 2x2 + -2x2 + -2y + 9y2 = -2x + -9xy + -2x2 Combine like terms: 2x2 + -2x2 = 0 0 + -2y + 9y2 = -2x + -9xy + -2x2 -2y + 9y2 = -2x + -9xy + -2x2 Add '2y' to each side of the equation. -2y + 2y + 9y2 = -2x + -9xy + -2x2 + 2y Combine like terms: -2y + 2y = 0 0 + 9y2 = -2x + -9xy + -2x2 + 2y 9y2 = -2x + -9xy + -2x2 + 2y Add '-9y2' to each side of the equation. 9y2 + -9y2 = -2x + -9xy + -2x2 + 2y + -9y2 Combine like terms: 9y2 + -9y2 = 0 0 = -2x + -9xy + -2x2 + 2y + -9y2 Simplifying 0 = -2x + -9xy + -2x2 + 2y + -9y2 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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