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Simplifying (6x + -5y + 4) * dy + (y + -2x + -1) * dx = 0 Reorder the terms: (4 + 6x + -5y) * dy + (y + -2x + -1) * dx = 0 Reorder the terms for easier multiplication: dy(4 + 6x + -5y) + (y + -2x + -1) * dx = 0 (4 * dy + 6x * dy + -5y * dy) + (y + -2x + -1) * dx = 0 Reorder the terms: (6dxy + 4dy + -5dy2) + (y + -2x + -1) * dx = 0 (6dxy + 4dy + -5dy2) + (y + -2x + -1) * dx = 0 Reorder the terms: 6dxy + 4dy + -5dy2 + (-1 + -2x + y) * dx = 0 Reorder the terms for easier multiplication: 6dxy + 4dy + -5dy2 + dx(-1 + -2x + y) = 0 6dxy + 4dy + -5dy2 + (-1 * dx + -2x * dx + y * dx) = 0 Reorder the terms: 6dxy + 4dy + -5dy2 + (-1dx + dxy + -2dx2) = 0 6dxy + 4dy + -5dy2 + (-1dx + dxy + -2dx2) = 0 Reorder the terms: -1dx + 6dxy + dxy + -2dx2 + 4dy + -5dy2 = 0 Combine like terms: 6dxy + dxy = 7dxy -1dx + 7dxy + -2dx2 + 4dy + -5dy2 = 0 Solving -1dx + 7dxy + -2dx2 + 4dy + -5dy2 = 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(-1x + 7xy + -2x2 + 4y + -5y2) = 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 '(-1x + 7xy + -2x2 + 4y + -5y2)' equal to zero and attempt to solve: Simplifying -1x + 7xy + -2x2 + 4y + -5y2 = 0 Solving -1x + 7xy + -2x2 + 4y + -5y2 = 0 Move all terms containing d to the left, all other terms to the right. Add 'x' to each side of the equation. -1x + 7xy + -2x2 + 4y + x + -5y2 = 0 + x Reorder the terms: -1x + x + 7xy + -2x2 + 4y + -5y2 = 0 + x Combine like terms: -1x + x = 0 0 + 7xy + -2x2 + 4y + -5y2 = 0 + x 7xy + -2x2 + 4y + -5y2 = 0 + x Remove the zero: 7xy + -2x2 + 4y + -5y2 = x Add '-7xy' to each side of the equation. 7xy + -2x2 + 4y + -7xy + -5y2 = x + -7xy Reorder the terms: 7xy + -7xy + -2x2 + 4y + -5y2 = x + -7xy Combine like terms: 7xy + -7xy = 0 0 + -2x2 + 4y + -5y2 = x + -7xy -2x2 + 4y + -5y2 = x + -7xy Add '2x2' to each side of the equation. -2x2 + 4y + 2x2 + -5y2 = x + -7xy + 2x2 Reorder the terms: -2x2 + 2x2 + 4y + -5y2 = x + -7xy + 2x2 Combine like terms: -2x2 + 2x2 = 0 0 + 4y + -5y2 = x + -7xy + 2x2 4y + -5y2 = x + -7xy + 2x2 Add '-4y' to each side of the equation. 4y + -4y + -5y2 = x + -7xy + 2x2 + -4y Combine like terms: 4y + -4y = 0 0 + -5y2 = x + -7xy + 2x2 + -4y -5y2 = x + -7xy + 2x2 + -4y Add '5y2' to each side of the equation. -5y2 + 5y2 = x + -7xy + 2x2 + -4y + 5y2 Combine like terms: -5y2 + 5y2 = 0 0 = x + -7xy + 2x2 + -4y + 5y2 Simplifying 0 = x + -7xy + 2x2 + -4y + 5y2 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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