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Simplifying (6x + 4y + -8) * dx = (x + y + -1) * dy Reorder the terms: (-8 + 6x + 4y) * dx = (x + y + -1) * dy Reorder the terms for easier multiplication: dx(-8 + 6x + 4y) = (x + y + -1) * dy (-8 * dx + 6x * dx + 4y * dx) = (x + y + -1) * dy Reorder the terms: (-8dx + 4dxy + 6dx2) = (x + y + -1) * dy (-8dx + 4dxy + 6dx2) = (x + y + -1) * dy Reorder the terms: -8dx + 4dxy + 6dx2 = (-1 + x + y) * dy Reorder the terms for easier multiplication: -8dx + 4dxy + 6dx2 = dy(-1 + x + y) -8dx + 4dxy + 6dx2 = (-1 * dy + x * dy + y * dy) Reorder the terms: -8dx + 4dxy + 6dx2 = (dxy + -1dy + dy2) -8dx + 4dxy + 6dx2 = (dxy + -1dy + dy2) Solving -8dx + 4dxy + 6dx2 = dxy + -1dy + dy2 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1dxy' to each side of the equation. -8dx + 4dxy + -1dxy + 6dx2 = dxy + -1dy + -1dxy + dy2 Combine like terms: 4dxy + -1dxy = 3dxy -8dx + 3dxy + 6dx2 = dxy + -1dy + -1dxy + dy2 Reorder the terms: -8dx + 3dxy + 6dx2 = dxy + -1dxy + -1dy + dy2 Combine like terms: dxy + -1dxy = 0 -8dx + 3dxy + 6dx2 = 0 + -1dy + dy2 -8dx + 3dxy + 6dx2 = -1dy + dy2 Add 'dy' to each side of the equation. -8dx + 3dxy + 6dx2 + dy = -1dy + dy + dy2 Combine like terms: -1dy + dy = 0 -8dx + 3dxy + 6dx2 + dy = 0 + dy2 -8dx + 3dxy + 6dx2 + dy = dy2 Add '-1dy2' to each side of the equation. -8dx + 3dxy + 6dx2 + dy + -1dy2 = dy2 + -1dy2 Combine like terms: dy2 + -1dy2 = 0 -8dx + 3dxy + 6dx2 + dy + -1dy2 = 0 Factor out the Greatest Common Factor (GCF), 'd'. d(-8x + 3xy + 6x2 + y + -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 '(-8x + 3xy + 6x2 + y + -1y2)' equal to zero and attempt to solve: Simplifying -8x + 3xy + 6x2 + y + -1y2 = 0 Solving -8x + 3xy + 6x2 + y + -1y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '8x' to each side of the equation. -8x + 3xy + 6x2 + y + 8x + -1y2 = 0 + 8x Reorder the terms: -8x + 8x + 3xy + 6x2 + y + -1y2 = 0 + 8x Combine like terms: -8x + 8x = 0 0 + 3xy + 6x2 + y + -1y2 = 0 + 8x 3xy + 6x2 + y + -1y2 = 0 + 8x Remove the zero: 3xy + 6x2 + y + -1y2 = 8x Add '-3xy' to each side of the equation. 3xy + 6x2 + y + -3xy + -1y2 = 8x + -3xy Reorder the terms: 3xy + -3xy + 6x2 + y + -1y2 = 8x + -3xy Combine like terms: 3xy + -3xy = 0 0 + 6x2 + y + -1y2 = 8x + -3xy 6x2 + y + -1y2 = 8x + -3xy Add '-6x2' to each side of the equation. 6x2 + y + -6x2 + -1y2 = 8x + -3xy + -6x2 Reorder the terms: 6x2 + -6x2 + y + -1y2 = 8x + -3xy + -6x2 Combine like terms: 6x2 + -6x2 = 0 0 + y + -1y2 = 8x + -3xy + -6x2 y + -1y2 = 8x + -3xy + -6x2 Add '-1y' to each side of the equation. y + -1y + -1y2 = 8x + -3xy + -6x2 + -1y Combine like terms: y + -1y = 0 0 + -1y2 = 8x + -3xy + -6x2 + -1y -1y2 = 8x + -3xy + -6x2 + -1y Add 'y2' to each side of the equation. -1y2 + y2 = 8x + -3xy + -6x2 + -1y + y2 Combine like terms: -1y2 + y2 = 0 0 = 8x + -3xy + -6x2 + -1y + y2 Simplifying 0 = 8x + -3xy + -6x2 + -1y + 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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