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Simplifying (3x + 2y) * dy = (2x + -3y) * dx Reorder the terms for easier multiplication: dy(3x + 2y) = (2x + -3y) * dx (3x * dy + 2y * dy) = (2x + -3y) * dx (3dxy + 2dy2) = (2x + -3y) * dx Reorder the terms for easier multiplication: 3dxy + 2dy2 = dx(2x + -3y) 3dxy + 2dy2 = (2x * dx + -3y * dx) Reorder the terms: 3dxy + 2dy2 = (-3dxy + 2dx2) 3dxy + 2dy2 = (-3dxy + 2dx2) Solving 3dxy + 2dy2 = -3dxy + 2dx2 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '3dxy' to each side of the equation. 3dxy + 3dxy + 2dy2 = -3dxy + 3dxy + 2dx2 Combine like terms: 3dxy + 3dxy = 6dxy 6dxy + 2dy2 = -3dxy + 3dxy + 2dx2 Combine like terms: -3dxy + 3dxy = 0 6dxy + 2dy2 = 0 + 2dx2 6dxy + 2dy2 = 2dx2 Add '-2dx2' to each side of the equation. 6dxy + -2dx2 + 2dy2 = 2dx2 + -2dx2 Combine like terms: 2dx2 + -2dx2 = 0 6dxy + -2dx2 + 2dy2 = 0 Factor out the Greatest Common Factor (GCF), '2d'. 2d(3xy + -1x2 + y2) = 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 '(3xy + -1x2 + y2)' equal to zero and attempt to solve: Simplifying 3xy + -1x2 + y2 = 0 Solving 3xy + -1x2 + y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-3xy' to each side of the equation. 3xy + -1x2 + -3xy + y2 = 0 + -3xy Reorder the terms: 3xy + -3xy + -1x2 + y2 = 0 + -3xy Combine like terms: 3xy + -3xy = 0 0 + -1x2 + y2 = 0 + -3xy -1x2 + y2 = 0 + -3xy Remove the zero: -1x2 + y2 = -3xy Add 'x2' to each side of the equation. -1x2 + x2 + y2 = -3xy + x2 Combine like terms: -1x2 + x2 = 0 0 + y2 = -3xy + x2 y2 = -3xy + x2 Add '-1y2' to each side of the equation. y2 + -1y2 = -3xy + x2 + -1y2 Combine like terms: y2 + -1y2 = 0 0 = -3xy + x2 + -1y2 Simplifying 0 = -3xy + x2 + -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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