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Simplifying X(3xy + -4y3 + 6) * dx + (x3 + -6x2y2 + -1) * dy = 0 Reorder the terms: X(6 + 3xy + -4y3) * dx + (x3 + -6x2y2 + -1) * dy = 0 Reorder the terms for easier multiplication: X * dx(6 + 3xy + -4y3) + (x3 + -6x2y2 + -1) * dy = 0 Multiply X * dx dxX(6 + 3xy + -4y3) + (x3 + -6x2y2 + -1) * dy = 0 (6 * dxX + 3xy * dxX + -4y3 * dxX) + (x3 + -6x2y2 + -1) * dy = 0 Reorder the terms: (6dxX + -4dxy3X + 3dx2yX) + (x3 + -6x2y2 + -1) * dy = 0 (6dxX + -4dxy3X + 3dx2yX) + (x3 + -6x2y2 + -1) * dy = 0 Reorder the terms: 6dxX + -4dxy3X + 3dx2yX + (-1 + -6x2y2 + x3) * dy = 0 Reorder the terms for easier multiplication: 6dxX + -4dxy3X + 3dx2yX + dy(-1 + -6x2y2 + x3) = 0 6dxX + -4dxy3X + 3dx2yX + (-1 * dy + -6x2y2 * dy + x3 * dy) = 0 Reorder the terms: 6dxX + -4dxy3X + 3dx2yX + (-6dx2y3 + dx3y + -1dy) = 0 6dxX + -4dxy3X + 3dx2yX + (-6dx2y3 + dx3y + -1dy) = 0 Solving 6dxX + -4dxy3X + 3dx2yX + -6dx2y3 + dx3y + -1dy = 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(6xX + -4xy3X + 3x2yX + -6x2y3 + x3y + -1y) = 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 '(6xX + -4xy3X + 3x2yX + -6x2y3 + x3y + -1y)' equal to zero and attempt to solve: Simplifying 6xX + -4xy3X + 3x2yX + -6x2y3 + x3y + -1y = 0 Solving 6xX + -4xy3X + 3x2yX + -6x2y3 + x3y + -1y = 0 Move all terms containing d to the left, all other terms to the right. Add '-6xX' to each side of the equation. 6xX + -4xy3X + 3x2yX + -6x2y3 + x3y + -6xX + -1y = 0 + -6xX Reorder the terms: 6xX + -6xX + -4xy3X + 3x2yX + -6x2y3 + x3y + -1y = 0 + -6xX Combine like terms: 6xX + -6xX = 0 0 + -4xy3X + 3x2yX + -6x2y3 + x3y + -1y = 0 + -6xX -4xy3X + 3x2yX + -6x2y3 + x3y + -1y = 0 + -6xX Remove the zero: -4xy3X + 3x2yX + -6x2y3 + x3y + -1y = -6xX Add '4xy3X' to each side of the equation. -4xy3X + 3x2yX + -6x2y3 + x3y + 4xy3X + -1y = -6xX + 4xy3X Reorder the terms: -4xy3X + 4xy3X + 3x2yX + -6x2y3 + x3y + -1y = -6xX + 4xy3X Combine like terms: -4xy3X + 4xy3X = 0 0 + 3x2yX + -6x2y3 + x3y + -1y = -6xX + 4xy3X 3x2yX + -6x2y3 + x3y + -1y = -6xX + 4xy3X Add '-3x2yX' to each side of the equation. 3x2yX + -6x2y3 + x3y + -3x2yX + -1y = -6xX + 4xy3X + -3x2yX Reorder the terms: 3x2yX + -3x2yX + -6x2y3 + x3y + -1y = -6xX + 4xy3X + -3x2yX Combine like terms: 3x2yX + -3x2yX = 0 0 + -6x2y3 + x3y + -1y = -6xX + 4xy3X + -3x2yX -6x2y3 + x3y + -1y = -6xX + 4xy3X + -3x2yX Add '6x2y3' to each side of the equation. -6x2y3 + x3y + 6x2y3 + -1y = -6xX + 4xy3X + -3x2yX + 6x2y3 Reorder the terms: -6x2y3 + 6x2y3 + x3y + -1y = -6xX + 4xy3X + -3x2yX + 6x2y3 Combine like terms: -6x2y3 + 6x2y3 = 0 0 + x3y + -1y = -6xX + 4xy3X + -3x2yX + 6x2y3 x3y + -1y = -6xX + 4xy3X + -3x2yX + 6x2y3 Add '-1x3y' to each side of the equation. x3y + -1x3y + -1y = -6xX + 4xy3X + -3x2yX + 6x2y3 + -1x3y Combine like terms: x3y + -1x3y = 0 0 + -1y = -6xX + 4xy3X + -3x2yX + 6x2y3 + -1x3y -1y = -6xX + 4xy3X + -3x2yX + 6x2y3 + -1x3y Add 'y' to each side of the equation. -1y + y = -6xX + 4xy3X + -3x2yX + 6x2y3 + -1x3y + y Combine like terms: -1y + y = 0 0 = -6xX + 4xy3X + -3x2yX + 6x2y3 + -1x3y + y Simplifying 0 = -6xX + 4xy3X + -3x2yX + 6x2y3 + -1x3y + 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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