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Simplifying (2x + 3y + -5) * dx + (3x + -1y + -2) * dy = 0 Reorder the terms: (-5 + 2x + 3y) * dx + (3x + -1y + -2) * dy = 0 Reorder the terms for easier multiplication: dx(-5 + 2x + 3y) + (3x + -1y + -2) * dy = 0 (-5 * dx + 2x * dx + 3y * dx) + (3x + -1y + -2) * dy = 0 Reorder the terms: (-5dx + 3dxy + 2dx2) + (3x + -1y + -2) * dy = 0 (-5dx + 3dxy + 2dx2) + (3x + -1y + -2) * dy = 0 Reorder the terms: -5dx + 3dxy + 2dx2 + (-2 + 3x + -1y) * dy = 0 Reorder the terms for easier multiplication: -5dx + 3dxy + 2dx2 + dy(-2 + 3x + -1y) = 0 -5dx + 3dxy + 2dx2 + (-2 * dy + 3x * dy + -1y * dy) = 0 Reorder the terms: -5dx + 3dxy + 2dx2 + (3dxy + -2dy + -1dy2) = 0 -5dx + 3dxy + 2dx2 + (3dxy + -2dy + -1dy2) = 0 Reorder the terms: -5dx + 3dxy + 3dxy + 2dx2 + -2dy + -1dy2 = 0 Combine like terms: 3dxy + 3dxy = 6dxy -5dx + 6dxy + 2dx2 + -2dy + -1dy2 = 0 Solving -5dx + 6dxy + 2dx2 + -2dy + -1dy2 = 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 + 6xy + 2x2 + -2y + -1y2) = 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 + -2y + -1y2)' equal to zero and attempt to solve: Simplifying -5x + 6xy + 2x2 + -2y + -1y2 = 0 Solving -5x + 6xy + 2x2 + -2y + -1y2 = 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 + -2y + 5x + -1y2 = 0 + 5x Reorder the terms: -5x + 5x + 6xy + 2x2 + -2y + -1y2 = 0 + 5x Combine like terms: -5x + 5x = 0 0 + 6xy + 2x2 + -2y + -1y2 = 0 + 5x 6xy + 2x2 + -2y + -1y2 = 0 + 5x Remove the zero: 6xy + 2x2 + -2y + -1y2 = 5x Add '-6xy' to each side of the equation. 6xy + 2x2 + -2y + -6xy + -1y2 = 5x + -6xy Reorder the terms: 6xy + -6xy + 2x2 + -2y + -1y2 = 5x + -6xy Combine like terms: 6xy + -6xy = 0 0 + 2x2 + -2y + -1y2 = 5x + -6xy 2x2 + -2y + -1y2 = 5x + -6xy Add '-2x2' to each side of the equation. 2x2 + -2y + -2x2 + -1y2 = 5x + -6xy + -2x2 Reorder the terms: 2x2 + -2x2 + -2y + -1y2 = 5x + -6xy + -2x2 Combine like terms: 2x2 + -2x2 = 0 0 + -2y + -1y2 = 5x + -6xy + -2x2 -2y + -1y2 = 5x + -6xy + -2x2 Add '2y' to each side of the equation. -2y + 2y + -1y2 = 5x + -6xy + -2x2 + 2y Combine like terms: -2y + 2y = 0 0 + -1y2 = 5x + -6xy + -2x2 + 2y -1y2 = 5x + -6xy + -2x2 + 2y Add 'y2' to each side of the equation. -1y2 + y2 = 5x + -6xy + -2x2 + 2y + y2 Combine like terms: -1y2 + y2 = 0 0 = 5x + -6xy + -2x2 + 2y + y2 Simplifying 0 = 5x + -6xy + -2x2 + 2y + y2 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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