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Simplifying ((y2) + -1(2xy) + (6x)) * dx + -1((x2) + -1(2xy) + (2)) * dy = 0 (y2 + -1(2xy) + (6x)) * dx + -1((x2) + -1(2xy) + (2)) * dy = 0 Remove parenthesis around (2xy) (y2 + -1 * 2xy + (6x)) * dx + -1((x2) + -1(2xy) + (2)) * dy = 0 Multiply -1 * 2 (y2 + -2xy + (6x)) * dx + -1((x2) + -1(2xy) + (2)) * dy = 0 Reorder the terms: ((6x) + -2xy + y2) * dx + -1((x2) + -1(2xy) + (2)) * dy = 0 Reorder the terms for easier multiplication: dx((6x) + -2xy + y2) + -1((x2) + -1(2xy) + (2)) * dy = 0 ((6x) * dx + -2xy * dx + y2 * dx) + -1((x2) + -1(2xy) + (2)) * dy = 0 Reorder the terms: (dxy2 + 6dx2 + -2dx2y) + -1((x2) + -1(2xy) + (2)) * dy = 0 (dxy2 + 6dx2 + -2dx2y) + -1((x2) + -1(2xy) + (2)) * dy = 0 dxy2 + 6dx2 + -2dx2y + -1(x2 + -1(2xy) + (2)) * dy = 0 Remove parenthesis around (2xy) dxy2 + 6dx2 + -2dx2y + -1(x2 + -1 * 2xy + (2)) * dy = 0 Multiply -1 * 2 dxy2 + 6dx2 + -2dx2y + -1(x2 + -2xy + (2)) * dy = 0 dxy2 + 6dx2 + -2dx2y + -1(x2 + -2xy + 2) * dy = 0 Reorder the terms: dxy2 + 6dx2 + -2dx2y + -1(2 + -2xy + x2) * dy = 0 Reorder the terms for easier multiplication: dxy2 + 6dx2 + -2dx2y + -1dy(2 + -2xy + x2) = 0 dxy2 + 6dx2 + -2dx2y + (2 * -1dy + -2xy * -1dy + x2 * -1dy) = 0 Reorder the terms: dxy2 + 6dx2 + -2dx2y + (2dxy2 + -1dx2y + -2dy) = 0 dxy2 + 6dx2 + -2dx2y + (2dxy2 + -1dx2y + -2dy) = 0 Reorder the terms: dxy2 + 2dxy2 + 6dx2 + -2dx2y + -1dx2y + -2dy = 0 Combine like terms: dxy2 + 2dxy2 = 3dxy2 3dxy2 + 6dx2 + -2dx2y + -1dx2y + -2dy = 0 Combine like terms: -2dx2y + -1dx2y = -3dx2y 3dxy2 + 6dx2 + -3dx2y + -2dy = 0 Solving 3dxy2 + 6dx2 + -3dx2y + -2dy = 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(3xy2 + 6x2 + -3x2y + -2y) = 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 '(3xy2 + 6x2 + -3x2y + -2y)' equal to zero and attempt to solve: Simplifying 3xy2 + 6x2 + -3x2y + -2y = 0 Solving 3xy2 + 6x2 + -3x2y + -2y = 0 Move all terms containing d to the left, all other terms to the right. Add '-3xy2' to each side of the equation. 3xy2 + 6x2 + -3x2y + -3xy2 + -2y = 0 + -3xy2 Reorder the terms: 3xy2 + -3xy2 + 6x2 + -3x2y + -2y = 0 + -3xy2 Combine like terms: 3xy2 + -3xy2 = 0 0 + 6x2 + -3x2y + -2y = 0 + -3xy2 6x2 + -3x2y + -2y = 0 + -3xy2 Remove the zero: 6x2 + -3x2y + -2y = -3xy2 Add '-6x2' to each side of the equation. 6x2 + -3x2y + -6x2 + -2y = -3xy2 + -6x2 Reorder the terms: 6x2 + -6x2 + -3x2y + -2y = -3xy2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 0 + -3x2y + -2y = -3xy2 + -6x2 -3x2y + -2y = -3xy2 + -6x2 Add '3x2y' to each side of the equation. -3x2y + 3x2y + -2y = -3xy2 + -6x2 + 3x2y Combine like terms: -3x2y + 3x2y = 0 0 + -2y = -3xy2 + -6x2 + 3x2y -2y = -3xy2 + -6x2 + 3x2y Add '2y' to each side of the equation. -2y + 2y = -3xy2 + -6x2 + 3x2y + 2y Combine like terms: -2y + 2y = 0 0 = -3xy2 + -6x2 + 3x2y + 2y Simplifying 0 = -3xy2 + -6x2 + 3x2y + 2y 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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