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Simplifying (5x + 3y + -1) * dx = (4y + -3x + -5) * dy Reorder the terms: (-1 + 5x + 3y) * dx = (4y + -3x + -5) * dy Reorder the terms for easier multiplication: dx(-1 + 5x + 3y) = (4y + -3x + -5) * dy (-1 * dx + 5x * dx + 3y * dx) = (4y + -3x + -5) * dy Reorder the terms: (-1dx + 3dxy + 5dx2) = (4y + -3x + -5) * dy (-1dx + 3dxy + 5dx2) = (4y + -3x + -5) * dy Reorder the terms: -1dx + 3dxy + 5dx2 = (-5 + -3x + 4y) * dy Reorder the terms for easier multiplication: -1dx + 3dxy + 5dx2 = dy(-5 + -3x + 4y) -1dx + 3dxy + 5dx2 = (-5 * dy + -3x * dy + 4y * dy) Reorder the terms: -1dx + 3dxy + 5dx2 = (-3dxy + -5dy + 4dy2) -1dx + 3dxy + 5dx2 = (-3dxy + -5dy + 4dy2) Solving -1dx + 3dxy + 5dx2 = -3dxy + -5dy + 4dy2 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '3dxy' to each side of the equation. -1dx + 3dxy + 3dxy + 5dx2 = -3dxy + -5dy + 3dxy + 4dy2 Combine like terms: 3dxy + 3dxy = 6dxy -1dx + 6dxy + 5dx2 = -3dxy + -5dy + 3dxy + 4dy2 Reorder the terms: -1dx + 6dxy + 5dx2 = -3dxy + 3dxy + -5dy + 4dy2 Combine like terms: -3dxy + 3dxy = 0 -1dx + 6dxy + 5dx2 = 0 + -5dy + 4dy2 -1dx + 6dxy + 5dx2 = -5dy + 4dy2 Add '5dy' to each side of the equation. -1dx + 6dxy + 5dx2 + 5dy = -5dy + 5dy + 4dy2 Combine like terms: -5dy + 5dy = 0 -1dx + 6dxy + 5dx2 + 5dy = 0 + 4dy2 -1dx + 6dxy + 5dx2 + 5dy = 4dy2 Add '-4dy2' to each side of the equation. -1dx + 6dxy + 5dx2 + 5dy + -4dy2 = 4dy2 + -4dy2 Combine like terms: 4dy2 + -4dy2 = 0 -1dx + 6dxy + 5dx2 + 5dy + -4dy2 = 0 Factor out the Greatest Common Factor (GCF), 'd'. d(-1x + 6xy + 5x2 + 5y + -4y2) = 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 + 6xy + 5x2 + 5y + -4y2)' equal to zero and attempt to solve: Simplifying -1x + 6xy + 5x2 + 5y + -4y2 = 0 Solving -1x + 6xy + 5x2 + 5y + -4y2 = 0 Move all terms containing d to the left, all other terms to the right. Add 'x' to each side of the equation. -1x + 6xy + 5x2 + 5y + x + -4y2 = 0 + x Reorder the terms: -1x + x + 6xy + 5x2 + 5y + -4y2 = 0 + x Combine like terms: -1x + x = 0 0 + 6xy + 5x2 + 5y + -4y2 = 0 + x 6xy + 5x2 + 5y + -4y2 = 0 + x Remove the zero: 6xy + 5x2 + 5y + -4y2 = x Add '-6xy' to each side of the equation. 6xy + 5x2 + 5y + -6xy + -4y2 = x + -6xy Reorder the terms: 6xy + -6xy + 5x2 + 5y + -4y2 = x + -6xy Combine like terms: 6xy + -6xy = 0 0 + 5x2 + 5y + -4y2 = x + -6xy 5x2 + 5y + -4y2 = x + -6xy Add '-5x2' to each side of the equation. 5x2 + 5y + -5x2 + -4y2 = x + -6xy + -5x2 Reorder the terms: 5x2 + -5x2 + 5y + -4y2 = x + -6xy + -5x2 Combine like terms: 5x2 + -5x2 = 0 0 + 5y + -4y2 = x + -6xy + -5x2 5y + -4y2 = x + -6xy + -5x2 Add '-5y' to each side of the equation. 5y + -5y + -4y2 = x + -6xy + -5x2 + -5y Combine like terms: 5y + -5y = 0 0 + -4y2 = x + -6xy + -5x2 + -5y -4y2 = x + -6xy + -5x2 + -5y Add '4y2' to each side of the equation. -4y2 + 4y2 = x + -6xy + -5x2 + -5y + 4y2 Combine like terms: -4y2 + 4y2 = 0 0 = x + -6xy + -5x2 + -5y + 4y2 Simplifying 0 = x + -6xy + -5x2 + -5y + 4y2 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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