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