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