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