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Simplifying (x + -1y) * dx + (3x2 + y) * dy = 0 Reorder the terms for easier multiplication: dx(x + -1y) + (3x2 + y) * dy = 0 (x * dx + -1y * dx) + (3x2 + y) * dy = 0 Reorder the terms: (-1dxy + dx2) + (3x2 + y) * dy = 0 (-1dxy + dx2) + (3x2 + y) * dy = 0 Reorder the terms for easier multiplication: -1dxy + dx2 + dy(3x2 + y) = 0 -1dxy + dx2 + (3x2 * dy + y * dy) = 0 -1dxy + dx2 + (3dx2y + dy2) = 0 Solving -1dxy + dx2 + 3dx2y + dy2 = 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(-1xy + x2 + 3x2y + 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 + x2 + 3x2y + y2)' equal to zero and attempt to solve: Simplifying -1xy + x2 + 3x2y + y2 = 0 Solving -1xy + x2 + 3x2y + 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 + x2 + 3x2y + xy + y2 = 0 + xy Reorder the terms: -1xy + xy + x2 + 3x2y + y2 = 0 + xy Combine like terms: -1xy + xy = 0 0 + x2 + 3x2y + y2 = 0 + xy x2 + 3x2y + y2 = 0 + xy Remove the zero: x2 + 3x2y + y2 = xy Add '-1x2' to each side of the equation. x2 + 3x2y + -1x2 + y2 = xy + -1x2 Reorder the terms: x2 + -1x2 + 3x2y + y2 = xy + -1x2 Combine like terms: x2 + -1x2 = 0 0 + 3x2y + y2 = xy + -1x2 3x2y + y2 = xy + -1x2 Add '-3x2y' to each side of the equation. 3x2y + -3x2y + y2 = xy + -1x2 + -3x2y Combine like terms: 3x2y + -3x2y = 0 0 + y2 = xy + -1x2 + -3x2y y2 = xy + -1x2 + -3x2y Add '-1y2' to each side of the equation. y2 + -1y2 = xy + -1x2 + -3x2y + -1y2 Combine like terms: y2 + -1y2 = 0 0 = xy + -1x2 + -3x2y + -1y2 Simplifying 0 = xy + -1x2 + -3x2y + -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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