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Simplifying (4x + -6y + -1) * dx(3y + -2x + -2) * dy = 0 Reorder the terms: (-1 + 4x + -6y) * dx(3y + -2x + -2) * dy = 0 Reorder the terms: (-1 + 4x + -6y) * dx(-2 + -2x + 3y) * dy = 0 Reorder the terms for easier multiplication: dx * dy(-1 + 4x + -6y)(-2 + -2x + 3y) = 0 Multiply dx * dy d2xy(-1 + 4x + -6y)(-2 + -2x + 3y) = 0 Multiply (-1 + 4x + -6y) * (-2 + -2x + 3y) d2xy(-1(-2 + -2x + 3y) + 4x * (-2 + -2x + 3y) + -6y * (-2 + -2x + 3y)) = 0 d2xy((-2 * -1 + -2x * -1 + 3y * -1) + 4x * (-2 + -2x + 3y) + -6y * (-2 + -2x + 3y)) = 0 d2xy((2 + 2x + -3y) + 4x * (-2 + -2x + 3y) + -6y * (-2 + -2x + 3y)) = 0 d2xy(2 + 2x + -3y + (-2 * 4x + -2x * 4x + 3y * 4x) + -6y * (-2 + -2x + 3y)) = 0 Reorder the terms: d2xy(2 + 2x + -3y + (-8x + 12xy + -8x2) + -6y * (-2 + -2x + 3y)) = 0 d2xy(2 + 2x + -3y + (-8x + 12xy + -8x2) + -6y * (-2 + -2x + 3y)) = 0 d2xy(2 + 2x + -3y + -8x + 12xy + -8x2 + (-2 * -6y + -2x * -6y + 3y * -6y)) = 0 Reorder the terms: d2xy(2 + 2x + -3y + -8x + 12xy + -8x2 + (12xy + 12y + -18y2)) = 0 d2xy(2 + 2x + -3y + -8x + 12xy + -8x2 + (12xy + 12y + -18y2)) = 0 Reorder the terms: d2xy(2 + 2x + -8x + 12xy + 12xy + -8x2 + -3y + 12y + -18y2) = 0 Combine like terms: 2x + -8x = -6x d2xy(2 + -6x + 12xy + 12xy + -8x2 + -3y + 12y + -18y2) = 0 Combine like terms: 12xy + 12xy = 24xy d2xy(2 + -6x + 24xy + -8x2 + -3y + 12y + -18y2) = 0 Combine like terms: -3y + 12y = 9y d2xy(2 + -6x + 24xy + -8x2 + 9y + -18y2) = 0 (2 * d2xy + -6x * d2xy + 24xy * d2xy + -8x2 * d2xy + 9y * d2xy + -18y2 * d2xy) = 0 Reorder the terms: (2d2xy + 9d2xy2 + -18d2xy3 + -6d2x2y + 24d2x2y2 + -8d2x3y) = 0 (2d2xy + 9d2xy2 + -18d2xy3 + -6d2x2y + 24d2x2y2 + -8d2x3y) = 0 Solving 2d2xy + 9d2xy2 + -18d2xy3 + -6d2x2y + 24d2x2y2 + -8d2x3y = 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), 'd2xy'. d2xy(2 + 9y + -18y2 + -6x + 24xy + -8x2) = 0Subproblem 1
Set the factor 'd2xy' equal to zero and attempt to solve: Simplifying d2xy = 0 Solving d2xy = 0 Move all terms containing d to the left, all other terms to the right. Simplifying d2xy = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(2 + 9y + -18y2 + -6x + 24xy + -8x2)' equal to zero and attempt to solve: Simplifying 2 + 9y + -18y2 + -6x + 24xy + -8x2 = 0 Reorder the terms: 2 + -6x + 24xy + -8x2 + 9y + -18y2 = 0 Solving 2 + -6x + 24xy + -8x2 + 9y + -18y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -6x + 24xy + -8x2 + 9y + -2 + -18y2 = 0 + -2 Reorder the terms: 2 + -2 + -6x + 24xy + -8x2 + 9y + -18y2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -6x + 24xy + -8x2 + 9y + -18y2 = 0 + -2 -6x + 24xy + -8x2 + 9y + -18y2 = 0 + -2 Combine like terms: 0 + -2 = -2 -6x + 24xy + -8x2 + 9y + -18y2 = -2 Add '6x' to each side of the equation. -6x + 24xy + -8x2 + 9y + 6x + -18y2 = -2 + 6x Reorder the terms: -6x + 6x + 24xy + -8x2 + 9y + -18y2 = -2 + 6x Combine like terms: -6x + 6x = 0 0 + 24xy + -8x2 + 9y + -18y2 = -2 + 6x 24xy + -8x2 + 9y + -18y2 = -2 + 6x Add '-24xy' to each side of the equation. 24xy + -8x2 + 9y + -24xy + -18y2 = -2 + 6x + -24xy Reorder the terms: 24xy + -24xy + -8x2 + 9y + -18y2 = -2 + 6x + -24xy Combine like terms: 24xy + -24xy = 0 0 + -8x2 + 9y + -18y2 = -2 + 6x + -24xy -8x2 + 9y + -18y2 = -2 + 6x + -24xy Add '8x2' to each side of the equation. -8x2 + 9y + 8x2 + -18y2 = -2 + 6x + -24xy + 8x2 Reorder the terms: -8x2 + 8x2 + 9y + -18y2 = -2 + 6x + -24xy + 8x2 Combine like terms: -8x2 + 8x2 = 0 0 + 9y + -18y2 = -2 + 6x + -24xy + 8x2 9y + -18y2 = -2 + 6x + -24xy + 8x2 Add '-9y' to each side of the equation. 9y + -9y + -18y2 = -2 + 6x + -24xy + 8x2 + -9y Combine like terms: 9y + -9y = 0 0 + -18y2 = -2 + 6x + -24xy + 8x2 + -9y -18y2 = -2 + 6x + -24xy + 8x2 + -9y Add '18y2' to each side of the equation. -18y2 + 18y2 = -2 + 6x + -24xy + 8x2 + -9y + 18y2 Combine like terms: -18y2 + 18y2 = 0 0 = -2 + 6x + -24xy + 8x2 + -9y + 18y2 Simplifying 0 = -2 + 6x + -24xy + 8x2 + -9y + 18y2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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