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