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Simplifying (2x + 3y) * dx = (4x + -1y + 5) * dy Reorder the terms for easier multiplication: dx(2x + 3y) = (4x + -1y + 5) * dy (2x * dx + 3y * dx) = (4x + -1y + 5) * dy Reorder the terms: (3dxy + 2dx2) = (4x + -1y + 5) * dy (3dxy + 2dx2) = (4x + -1y + 5) * dy Reorder the terms: 3dxy + 2dx2 = (5 + 4x + -1y) * dy Reorder the terms for easier multiplication: 3dxy + 2dx2 = dy(5 + 4x + -1y) 3dxy + 2dx2 = (5 * dy + 4x * dy + -1y * dy) Reorder the terms: 3dxy + 2dx2 = (4dxy + 5dy + -1dy2) 3dxy + 2dx2 = (4dxy + 5dy + -1dy2) Solving 3dxy + 2dx2 = 4dxy + 5dy + -1dy2 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-4dxy' to each side of the equation. 3dxy + -4dxy + 2dx2 = 4dxy + 5dy + -4dxy + -1dy2 Combine like terms: 3dxy + -4dxy = -1dxy -1dxy + 2dx2 = 4dxy + 5dy + -4dxy + -1dy2 Reorder the terms: -1dxy + 2dx2 = 4dxy + -4dxy + 5dy + -1dy2 Combine like terms: 4dxy + -4dxy = 0 -1dxy + 2dx2 = 0 + 5dy + -1dy2 -1dxy + 2dx2 = 5dy + -1dy2 Add '-5dy' to each side of the equation. -1dxy + 2dx2 + -5dy = 5dy + -5dy + -1dy2 Combine like terms: 5dy + -5dy = 0 -1dxy + 2dx2 + -5dy = 0 + -1dy2 -1dxy + 2dx2 + -5dy = -1dy2 Add 'dy2' to each side of the equation. -1dxy + 2dx2 + -5dy + dy2 = -1dy2 + dy2 Combine like terms: -1dy2 + dy2 = 0 -1dxy + 2dx2 + -5dy + dy2 = 0 Factor out the Greatest Common Factor (GCF), 'd'. d(-1xy + 2x2 + -5y + y2) = 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 '(-1xy + 2x2 + -5y + y2)' equal to zero and attempt to solve: Simplifying -1xy + 2x2 + -5y + y2 = 0 Solving -1xy + 2x2 + -5y + y2 = 0 Move all terms containing d to the left, all other terms to the right. Add 'xy' to each side of the equation. -1xy + 2x2 + -5y + xy + y2 = 0 + xy Reorder the terms: -1xy + xy + 2x2 + -5y + y2 = 0 + xy Combine like terms: -1xy + xy = 0 0 + 2x2 + -5y + y2 = 0 + xy 2x2 + -5y + y2 = 0 + xy Remove the zero: 2x2 + -5y + y2 = xy Add '-2x2' to each side of the equation. 2x2 + -5y + -2x2 + y2 = xy + -2x2 Reorder the terms: 2x2 + -2x2 + -5y + y2 = xy + -2x2 Combine like terms: 2x2 + -2x2 = 0 0 + -5y + y2 = xy + -2x2 -5y + y2 = xy + -2x2 Add '5y' to each side of the equation. -5y + 5y + y2 = xy + -2x2 + 5y Combine like terms: -5y + 5y = 0 0 + y2 = xy + -2x2 + 5y y2 = xy + -2x2 + 5y Add '-1y2' to each side of the equation. y2 + -1y2 = xy + -2x2 + 5y + -1y2 Combine like terms: y2 + -1y2 = 0 0 = xy + -2x2 + 5y + -1y2 Simplifying 0 = xy + -2x2 + 5y + -1y2 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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