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Simplifying (4y + -2)(x + -2) * dy + (3x2 + -4x + -2) * dx = 0 Reorder the terms: (-2 + 4y)(x + -2) * dy + (3x2 + -4x + -2) * dx = 0 Reorder the terms: (-2 + 4y)(-2 + x) * dy + (3x2 + -4x + -2) * dx = 0 Reorder the terms for easier multiplication: dy(-2 + 4y)(-2 + x) + (3x2 + -4x + -2) * dx = 0 Multiply (-2 + 4y) * (-2 + x) dy(-2(-2 + x) + 4y * (-2 + x)) + (3x2 + -4x + -2) * dx = 0 dy((-2 * -2 + x * -2) + 4y * (-2 + x)) + (3x2 + -4x + -2) * dx = 0 dy((4 + -2x) + 4y * (-2 + x)) + (3x2 + -4x + -2) * dx = 0 dy(4 + -2x + (-2 * 4y + x * 4y)) + (3x2 + -4x + -2) * dx = 0 Reorder the terms: dy(4 + -2x + (4xy + -8y)) + (3x2 + -4x + -2) * dx = 0 dy(4 + -2x + (4xy + -8y)) + (3x2 + -4x + -2) * dx = 0 dy(4 + -2x + 4xy + -8y) + (3x2 + -4x + -2) * dx = 0 (4 * dy + -2x * dy + 4xy * dy + -8y * dy) + (3x2 + -4x + -2) * dx = 0 Reorder the terms: (-2dxy + 4dxy2 + 4dy + -8dy2) + (3x2 + -4x + -2) * dx = 0 (-2dxy + 4dxy2 + 4dy + -8dy2) + (3x2 + -4x + -2) * dx = 0 Reorder the terms: -2dxy + 4dxy2 + 4dy + -8dy2 + (-2 + -4x + 3x2) * dx = 0 Reorder the terms for easier multiplication: -2dxy + 4dxy2 + 4dy + -8dy2 + dx(-2 + -4x + 3x2) = 0 -2dxy + 4dxy2 + 4dy + -8dy2 + (-2 * dx + -4x * dx + 3x2 * dx) = 0 -2dxy + 4dxy2 + 4dy + -8dy2 + (-2dx + -4dx2 + 3dx3) = 0 Reorder the terms: -2dx + -2dxy + 4dxy2 + -4dx2 + 3dx3 + 4dy + -8dy2 = 0 Solving -2dx + -2dxy + 4dxy2 + -4dx2 + 3dx3 + 4dy + -8dy2 = 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(-2x + -2xy + 4xy2 + -4x2 + 3x3 + 4y + -8y2) = 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 '(-2x + -2xy + 4xy2 + -4x2 + 3x3 + 4y + -8y2)' equal to zero and attempt to solve: Simplifying -2x + -2xy + 4xy2 + -4x2 + 3x3 + 4y + -8y2 = 0 Solving -2x + -2xy + 4xy2 + -4x2 + 3x3 + 4y + -8y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '2x' to each side of the equation. -2x + -2xy + 4xy2 + -4x2 + 3x3 + 4y + 2x + -8y2 = 0 + 2x Reorder the terms: -2x + 2x + -2xy + 4xy2 + -4x2 + 3x3 + 4y + -8y2 = 0 + 2x Combine like terms: -2x + 2x = 0 0 + -2xy + 4xy2 + -4x2 + 3x3 + 4y + -8y2 = 0 + 2x -2xy + 4xy2 + -4x2 + 3x3 + 4y + -8y2 = 0 + 2x Remove the zero: -2xy + 4xy2 + -4x2 + 3x3 + 4y + -8y2 = 2x Add '2xy' to each side of the equation. -2xy + 4xy2 + -4x2 + 3x3 + 4y + 2xy + -8y2 = 2x + 2xy Reorder the terms: -2xy + 2xy + 4xy2 + -4x2 + 3x3 + 4y + -8y2 = 2x + 2xy Combine like terms: -2xy + 2xy = 0 0 + 4xy2 + -4x2 + 3x3 + 4y + -8y2 = 2x + 2xy 4xy2 + -4x2 + 3x3 + 4y + -8y2 = 2x + 2xy Add '-4xy2' to each side of the equation. 4xy2 + -4x2 + 3x3 + 4y + -4xy2 + -8y2 = 2x + 2xy + -4xy2 Reorder the terms: 4xy2 + -4xy2 + -4x2 + 3x3 + 4y + -8y2 = 2x + 2xy + -4xy2 Combine like terms: 4xy2 + -4xy2 = 0 0 + -4x2 + 3x3 + 4y + -8y2 = 2x + 2xy + -4xy2 -4x2 + 3x3 + 4y + -8y2 = 2x + 2xy + -4xy2 Add '4x2' to each side of the equation. -4x2 + 3x3 + 4y + 4x2 + -8y2 = 2x + 2xy + -4xy2 + 4x2 Reorder the terms: -4x2 + 4x2 + 3x3 + 4y + -8y2 = 2x + 2xy + -4xy2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 0 + 3x3 + 4y + -8y2 = 2x + 2xy + -4xy2 + 4x2 3x3 + 4y + -8y2 = 2x + 2xy + -4xy2 + 4x2 Add '-3x3' to each side of the equation. 3x3 + 4y + -3x3 + -8y2 = 2x + 2xy + -4xy2 + 4x2 + -3x3 Reorder the terms: 3x3 + -3x3 + 4y + -8y2 = 2x + 2xy + -4xy2 + 4x2 + -3x3 Combine like terms: 3x3 + -3x3 = 0 0 + 4y + -8y2 = 2x + 2xy + -4xy2 + 4x2 + -3x3 4y + -8y2 = 2x + 2xy + -4xy2 + 4x2 + -3x3 Add '-4y' to each side of the equation. 4y + -4y + -8y2 = 2x + 2xy + -4xy2 + 4x2 + -3x3 + -4y Combine like terms: 4y + -4y = 0 0 + -8y2 = 2x + 2xy + -4xy2 + 4x2 + -3x3 + -4y -8y2 = 2x + 2xy + -4xy2 + 4x2 + -3x3 + -4y Add '8y2' to each side of the equation. -8y2 + 8y2 = 2x + 2xy + -4xy2 + 4x2 + -3x3 + -4y + 8y2 Combine like terms: -8y2 + 8y2 = 0 0 = 2x + 2xy + -4xy2 + 4x2 + -3x3 + -4y + 8y2 Simplifying 0 = 2x + 2xy + -4xy2 + 4x2 + -3x3 + -4y + 8y2 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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