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