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Simplifying (2x + 3y + -5) * dy + (3x + 2y + -5) * dx = 0 Reorder the terms: (-5 + 2x + 3y) * dy + (3x + 2y + -5) * dx = 0 Reorder the terms for easier multiplication: dy(-5 + 2x + 3y) + (3x + 2y + -5) * dx = 0 (-5 * dy + 2x * dy + 3y * dy) + (3x + 2y + -5) * dx = 0 Reorder the terms: (2dxy + -5dy + 3dy2) + (3x + 2y + -5) * dx = 0 (2dxy + -5dy + 3dy2) + (3x + 2y + -5) * dx = 0 Reorder the terms: 2dxy + -5dy + 3dy2 + (-5 + 3x + 2y) * dx = 0 Reorder the terms for easier multiplication: 2dxy + -5dy + 3dy2 + dx(-5 + 3x + 2y) = 0 2dxy + -5dy + 3dy2 + (-5 * dx + 3x * dx + 2y * dx) = 0 Reorder the terms: 2dxy + -5dy + 3dy2 + (-5dx + 2dxy + 3dx2) = 0 2dxy + -5dy + 3dy2 + (-5dx + 2dxy + 3dx2) = 0 Reorder the terms: -5dx + 2dxy + 2dxy + 3dx2 + -5dy + 3dy2 = 0 Combine like terms: 2dxy + 2dxy = 4dxy -5dx + 4dxy + 3dx2 + -5dy + 3dy2 = 0 Solving -5dx + 4dxy + 3dx2 + -5dy + 3dy2 = 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(-5x + 4xy + 3x2 + -5y + 3y2) = 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 '(-5x + 4xy + 3x2 + -5y + 3y2)' equal to zero and attempt to solve: Simplifying -5x + 4xy + 3x2 + -5y + 3y2 = 0 Solving -5x + 4xy + 3x2 + -5y + 3y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '5x' to each side of the equation. -5x + 4xy + 3x2 + -5y + 5x + 3y2 = 0 + 5x Reorder the terms: -5x + 5x + 4xy + 3x2 + -5y + 3y2 = 0 + 5x Combine like terms: -5x + 5x = 0 0 + 4xy + 3x2 + -5y + 3y2 = 0 + 5x 4xy + 3x2 + -5y + 3y2 = 0 + 5x Remove the zero: 4xy + 3x2 + -5y + 3y2 = 5x Add '-4xy' to each side of the equation. 4xy + 3x2 + -5y + -4xy + 3y2 = 5x + -4xy Reorder the terms: 4xy + -4xy + 3x2 + -5y + 3y2 = 5x + -4xy Combine like terms: 4xy + -4xy = 0 0 + 3x2 + -5y + 3y2 = 5x + -4xy 3x2 + -5y + 3y2 = 5x + -4xy Add '-3x2' to each side of the equation. 3x2 + -5y + -3x2 + 3y2 = 5x + -4xy + -3x2 Reorder the terms: 3x2 + -3x2 + -5y + 3y2 = 5x + -4xy + -3x2 Combine like terms: 3x2 + -3x2 = 0 0 + -5y + 3y2 = 5x + -4xy + -3x2 -5y + 3y2 = 5x + -4xy + -3x2 Add '5y' to each side of the equation. -5y + 5y + 3y2 = 5x + -4xy + -3x2 + 5y Combine like terms: -5y + 5y = 0 0 + 3y2 = 5x + -4xy + -3x2 + 5y 3y2 = 5x + -4xy + -3x2 + 5y Add '-3y2' to each side of the equation. 3y2 + -3y2 = 5x + -4xy + -3x2 + 5y + -3y2 Combine like terms: 3y2 + -3y2 = 0 0 = 5x + -4xy + -3x2 + 5y + -3y2 Simplifying 0 = 5x + -4xy + -3x2 + 5y + -3y2 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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