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Simplifying (5 + -2y + -3x) * dy = (2x + 3y + -5) * dx Reorder the terms: (5 + -3x + -2y) * dy = (2x + 3y + -5) * dx Reorder the terms for easier multiplication: dy(5 + -3x + -2y) = (2x + 3y + -5) * dx (5 * dy + -3x * dy + -2y * dy) = (2x + 3y + -5) * dx Reorder the terms: (-3dxy + 5dy + -2dy2) = (2x + 3y + -5) * dx (-3dxy + 5dy + -2dy2) = (2x + 3y + -5) * dx Reorder the terms: -3dxy + 5dy + -2dy2 = (-5 + 2x + 3y) * dx Reorder the terms for easier multiplication: -3dxy + 5dy + -2dy2 = dx(-5 + 2x + 3y) -3dxy + 5dy + -2dy2 = (-5 * dx + 2x * dx + 3y * dx) Reorder the terms: -3dxy + 5dy + -2dy2 = (-5dx + 3dxy + 2dx2) -3dxy + 5dy + -2dy2 = (-5dx + 3dxy + 2dx2) Solving -3dxy + 5dy + -2dy2 = -5dx + 3dxy + 2dx2 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. -3dxy + 5dy + 5dx + -2dy2 = -5dx + 3dxy + 5dx + 2dx2 Reorder the terms: 5dx + -3dxy + 5dy + -2dy2 = -5dx + 3dxy + 5dx + 2dx2 Reorder the terms: 5dx + -3dxy + 5dy + -2dy2 = -5dx + 5dx + 3dxy + 2dx2 Combine like terms: -5dx + 5dx = 0 5dx + -3dxy + 5dy + -2dy2 = 0 + 3dxy + 2dx2 5dx + -3dxy + 5dy + -2dy2 = 3dxy + 2dx2 Add '-3dxy' to each side of the equation. 5dx + -3dxy + 5dy + -3dxy + -2dy2 = 3dxy + -3dxy + 2dx2 Reorder the terms: 5dx + -3dxy + -3dxy + 5dy + -2dy2 = 3dxy + -3dxy + 2dx2 Combine like terms: -3dxy + -3dxy = -6dxy 5dx + -6dxy + 5dy + -2dy2 = 3dxy + -3dxy + 2dx2 Combine like terms: 3dxy + -3dxy = 0 5dx + -6dxy + 5dy + -2dy2 = 0 + 2dx2 5dx + -6dxy + 5dy + -2dy2 = 2dx2 Add '-2dx2' to each side of the equation. 5dx + -6dxy + 5dy + -2dx2 + -2dy2 = 2dx2 + -2dx2 Reorder the terms: 5dx + -6dxy + -2dx2 + 5dy + -2dy2 = 2dx2 + -2dx2 Combine like terms: 2dx2 + -2dx2 = 0 5dx + -6dxy + -2dx2 + 5dy + -2dy2 = 0 Factor out the Greatest Common Factor (GCF), 'd'. d(5x + -6xy + -2x2 + 5y + -2y2) = 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 + -6xy + -2x2 + 5y + -2y2)' equal to zero and attempt to solve: Simplifying 5x + -6xy + -2x2 + 5y + -2y2 = 0 Solving 5x + -6xy + -2x2 + 5y + -2y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-5x' to each side of the equation. 5x + -6xy + -2x2 + 5y + -5x + -2y2 = 0 + -5x Reorder the terms: 5x + -5x + -6xy + -2x2 + 5y + -2y2 = 0 + -5x Combine like terms: 5x + -5x = 0 0 + -6xy + -2x2 + 5y + -2y2 = 0 + -5x -6xy + -2x2 + 5y + -2y2 = 0 + -5x Remove the zero: -6xy + -2x2 + 5y + -2y2 = -5x Add '6xy' to each side of the equation. -6xy + -2x2 + 5y + 6xy + -2y2 = -5x + 6xy Reorder the terms: -6xy + 6xy + -2x2 + 5y + -2y2 = -5x + 6xy Combine like terms: -6xy + 6xy = 0 0 + -2x2 + 5y + -2y2 = -5x + 6xy -2x2 + 5y + -2y2 = -5x + 6xy Add '2x2' to each side of the equation. -2x2 + 5y + 2x2 + -2y2 = -5x + 6xy + 2x2 Reorder the terms: -2x2 + 2x2 + 5y + -2y2 = -5x + 6xy + 2x2 Combine like terms: -2x2 + 2x2 = 0 0 + 5y + -2y2 = -5x + 6xy + 2x2 5y + -2y2 = -5x + 6xy + 2x2 Add '-5y' to each side of the equation. 5y + -5y + -2y2 = -5x + 6xy + 2x2 + -5y Combine like terms: 5y + -5y = 0 0 + -2y2 = -5x + 6xy + 2x2 + -5y -2y2 = -5x + 6xy + 2x2 + -5y Add '2y2' to each side of the equation. -2y2 + 2y2 = -5x + 6xy + 2x2 + -5y + 2y2 Combine like terms: -2y2 + 2y2 = 0 0 = -5x + 6xy + 2x2 + -5y + 2y2 Simplifying 0 = -5x + 6xy + 2x2 + -5y + 2y2 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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