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Simplifying (6x + 4y + -8) * dx + (x + y + -1) * dy = 0 Reorder the terms: (-8 + 6x + 4y) * dx + (x + y + -1) * dy = 0 Reorder the terms for easier multiplication: dx(-8 + 6x + 4y) + (x + y + -1) * dy = 0 (-8 * dx + 6x * dx + 4y * dx) + (x + y + -1) * dy = 0 Reorder the terms: (-8dx + 4dxy + 6dx2) + (x + y + -1) * dy = 0 (-8dx + 4dxy + 6dx2) + (x + y + -1) * dy = 0 Reorder the terms: -8dx + 4dxy + 6dx2 + (-1 + x + y) * dy = 0 Reorder the terms for easier multiplication: -8dx + 4dxy + 6dx2 + dy(-1 + x + y) = 0 -8dx + 4dxy + 6dx2 + (-1 * dy + x * dy + y * dy) = 0 Reorder the terms: -8dx + 4dxy + 6dx2 + (dxy + -1dy + dy2) = 0 -8dx + 4dxy + 6dx2 + (dxy + -1dy + dy2) = 0 Reorder the terms: -8dx + 4dxy + dxy + 6dx2 + -1dy + dy2 = 0 Combine like terms: 4dxy + dxy = 5dxy -8dx + 5dxy + 6dx2 + -1dy + dy2 = 0 Solving -8dx + 5dxy + 6dx2 + -1dy + dy2 = 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(-8x + 5xy + 6x2 + -1y + 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 '(-8x + 5xy + 6x2 + -1y + y2)' equal to zero and attempt to solve: Simplifying -8x + 5xy + 6x2 + -1y + y2 = 0 Solving -8x + 5xy + 6x2 + -1y + y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '8x' to each side of the equation. -8x + 5xy + 6x2 + -1y + 8x + y2 = 0 + 8x Reorder the terms: -8x + 8x + 5xy + 6x2 + -1y + y2 = 0 + 8x Combine like terms: -8x + 8x = 0 0 + 5xy + 6x2 + -1y + y2 = 0 + 8x 5xy + 6x2 + -1y + y2 = 0 + 8x Remove the zero: 5xy + 6x2 + -1y + y2 = 8x Add '-5xy' to each side of the equation. 5xy + 6x2 + -1y + -5xy + y2 = 8x + -5xy Reorder the terms: 5xy + -5xy + 6x2 + -1y + y2 = 8x + -5xy Combine like terms: 5xy + -5xy = 0 0 + 6x2 + -1y + y2 = 8x + -5xy 6x2 + -1y + y2 = 8x + -5xy Add '-6x2' to each side of the equation. 6x2 + -1y + -6x2 + y2 = 8x + -5xy + -6x2 Reorder the terms: 6x2 + -6x2 + -1y + y2 = 8x + -5xy + -6x2 Combine like terms: 6x2 + -6x2 = 0 0 + -1y + y2 = 8x + -5xy + -6x2 -1y + y2 = 8x + -5xy + -6x2 Add 'y' to each side of the equation. -1y + y + y2 = 8x + -5xy + -6x2 + y Combine like terms: -1y + y = 0 0 + y2 = 8x + -5xy + -6x2 + y y2 = 8x + -5xy + -6x2 + y Add '-1y2' to each side of the equation. y2 + -1y2 = 8x + -5xy + -6x2 + y + -1y2 Combine like terms: y2 + -1y2 = 0 0 = 8x + -5xy + -6x2 + y + -1y2 Simplifying 0 = 8x + -5xy + -6x2 + y + -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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