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Simplifying (3y + -2x) * dx + -1(2y + -1x) * dy = 0 Reorder the terms: (-2x + 3y) * dx + -1(2y + -1x) * dy = 0 Reorder the terms for easier multiplication: dx(-2x + 3y) + -1(2y + -1x) * dy = 0 (-2x * dx + 3y * dx) + -1(2y + -1x) * dy = 0 Reorder the terms: (3dxy + -2dx2) + -1(2y + -1x) * dy = 0 (3dxy + -2dx2) + -1(2y + -1x) * dy = 0 Reorder the terms: 3dxy + -2dx2 + -1(-1x + 2y) * dy = 0 Reorder the terms for easier multiplication: 3dxy + -2dx2 + -1dy(-1x + 2y) = 0 3dxy + -2dx2 + (-1x * -1dy + 2y * -1dy) = 0 3dxy + -2dx2 + (1dxy + -2dy2) = 0 Reorder the terms: 3dxy + 1dxy + -2dx2 + -2dy2 = 0 Combine like terms: 3dxy + 1dxy = 4dxy 4dxy + -2dx2 + -2dy2 = 0 Solving 4dxy + -2dx2 + -2dy2 = 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), '2d'. 2d(2xy + -1x2 + -1y2) = 0 Factor a trinomial. 2d((-1x + y)(x + -1y)) = 0 Ignore the factor 2.Subproblem 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 + y)' equal to zero and attempt to solve: Simplifying -1x + y = 0 Solving -1x + y = 0 Move all terms containing d to the left, all other terms to the right. Add 'x' to each side of the equation. -1x + x + y = 0 + x Combine like terms: -1x + x = 0 0 + y = 0 + x y = 0 + x Remove the zero: y = x Add '-1y' to each side of the equation. y + -1y = x + -1y Combine like terms: y + -1y = 0 0 = x + -1y Simplifying 0 = x + -1y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(x + -1y)' equal to zero and attempt to solve: Simplifying x + -1y = 0 Solving x + -1y = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x + -1y = 0 + -1x Combine like terms: x + -1x = 0 0 + -1y = 0 + -1x -1y = 0 + -1x Remove the zero: -1y = -1x Add 'y' to each side of the equation. -1y + y = -1x + y Combine like terms: -1y + y = 0 0 = -1x + y Simplifying 0 = -1x + y 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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