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Simplifying (4x + -6y + -1) * dx(3x + -2y + -2) * dy = 0 Reorder the terms: (-1 + 4x + -6y) * dx(3x + -2y + -2) * dy = 0 Reorder the terms: (-1 + 4x + -6y) * dx(-2 + 3x + -2y) * dy = 0 Reorder the terms for easier multiplication: dx * dy(-1 + 4x + -6y)(-2 + 3x + -2y) = 0 Multiply dx * dy d2xy(-1 + 4x + -6y)(-2 + 3x + -2y) = 0 Multiply (-1 + 4x + -6y) * (-2 + 3x + -2y) d2xy(-1(-2 + 3x + -2y) + 4x * (-2 + 3x + -2y) + -6y * (-2 + 3x + -2y)) = 0 d2xy((-2 * -1 + 3x * -1 + -2y * -1) + 4x * (-2 + 3x + -2y) + -6y * (-2 + 3x + -2y)) = 0 d2xy((2 + -3x + 2y) + 4x * (-2 + 3x + -2y) + -6y * (-2 + 3x + -2y)) = 0 d2xy(2 + -3x + 2y + (-2 * 4x + 3x * 4x + -2y * 4x) + -6y * (-2 + 3x + -2y)) = 0 Reorder the terms: d2xy(2 + -3x + 2y + (-8x + -8xy + 12x2) + -6y * (-2 + 3x + -2y)) = 0 d2xy(2 + -3x + 2y + (-8x + -8xy + 12x2) + -6y * (-2 + 3x + -2y)) = 0 d2xy(2 + -3x + 2y + -8x + -8xy + 12x2 + (-2 * -6y + 3x * -6y + -2y * -6y)) = 0 Reorder the terms: d2xy(2 + -3x + 2y + -8x + -8xy + 12x2 + (-18xy + 12y + 12y2)) = 0 d2xy(2 + -3x + 2y + -8x + -8xy + 12x2 + (-18xy + 12y + 12y2)) = 0 Reorder the terms: d2xy(2 + -3x + -8x + -8xy + -18xy + 12x2 + 2y + 12y + 12y2) = 0 Combine like terms: -3x + -8x = -11x d2xy(2 + -11x + -8xy + -18xy + 12x2 + 2y + 12y + 12y2) = 0 Combine like terms: -8xy + -18xy = -26xy d2xy(2 + -11x + -26xy + 12x2 + 2y + 12y + 12y2) = 0 Combine like terms: 2y + 12y = 14y d2xy(2 + -11x + -26xy + 12x2 + 14y + 12y2) = 0 (2 * d2xy + -11x * d2xy + -26xy * d2xy + 12x2 * d2xy + 14y * d2xy + 12y2 * d2xy) = 0 Reorder the terms: (2d2xy + 14d2xy2 + 12d2xy3 + -11d2x2y + -26d2x2y2 + 12d2x3y) = 0 (2d2xy + 14d2xy2 + 12d2xy3 + -11d2x2y + -26d2x2y2 + 12d2x3y) = 0 Solving 2d2xy + 14d2xy2 + 12d2xy3 + -11d2x2y + -26d2x2y2 + 12d2x3y = 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 + 14y + 12y2 + -11x + -26xy + 12x2) = 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 + 14y + 12y2 + -11x + -26xy + 12x2)' equal to zero and attempt to solve: Simplifying 2 + 14y + 12y2 + -11x + -26xy + 12x2 = 0 Reorder the terms: 2 + -11x + -26xy + 12x2 + 14y + 12y2 = 0 Solving 2 + -11x + -26xy + 12x2 + 14y + 12y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -11x + -26xy + 12x2 + 14y + -2 + 12y2 = 0 + -2 Reorder the terms: 2 + -2 + -11x + -26xy + 12x2 + 14y + 12y2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -11x + -26xy + 12x2 + 14y + 12y2 = 0 + -2 -11x + -26xy + 12x2 + 14y + 12y2 = 0 + -2 Combine like terms: 0 + -2 = -2 -11x + -26xy + 12x2 + 14y + 12y2 = -2 Add '11x' to each side of the equation. -11x + -26xy + 12x2 + 14y + 11x + 12y2 = -2 + 11x Reorder the terms: -11x + 11x + -26xy + 12x2 + 14y + 12y2 = -2 + 11x Combine like terms: -11x + 11x = 0 0 + -26xy + 12x2 + 14y + 12y2 = -2 + 11x -26xy + 12x2 + 14y + 12y2 = -2 + 11x Add '26xy' to each side of the equation. -26xy + 12x2 + 14y + 26xy + 12y2 = -2 + 11x + 26xy Reorder the terms: -26xy + 26xy + 12x2 + 14y + 12y2 = -2 + 11x + 26xy Combine like terms: -26xy + 26xy = 0 0 + 12x2 + 14y + 12y2 = -2 + 11x + 26xy 12x2 + 14y + 12y2 = -2 + 11x + 26xy Add '-12x2' to each side of the equation. 12x2 + 14y + -12x2 + 12y2 = -2 + 11x + 26xy + -12x2 Reorder the terms: 12x2 + -12x2 + 14y + 12y2 = -2 + 11x + 26xy + -12x2 Combine like terms: 12x2 + -12x2 = 0 0 + 14y + 12y2 = -2 + 11x + 26xy + -12x2 14y + 12y2 = -2 + 11x + 26xy + -12x2 Add '-14y' to each side of the equation. 14y + -14y + 12y2 = -2 + 11x + 26xy + -12x2 + -14y Combine like terms: 14y + -14y = 0 0 + 12y2 = -2 + 11x + 26xy + -12x2 + -14y 12y2 = -2 + 11x + 26xy + -12x2 + -14y Add '-12y2' to each side of the equation. 12y2 + -12y2 = -2 + 11x + 26xy + -12x2 + -14y + -12y2 Combine like terms: 12y2 + -12y2 = 0 0 = -2 + 11x + 26xy + -12x2 + -14y + -12y2 Simplifying 0 = -2 + 11x + 26xy + -12x2 + -14y + -12y2 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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