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Simplifying (6x + 4y + 1) * dx + (4x + 2y + 2) * dy = 0 Reorder the terms: (1 + 6x + 4y) * dx + (4x + 2y + 2) * dy = 0 Reorder the terms for easier multiplication: dx(1 + 6x + 4y) + (4x + 2y + 2) * dy = 0 (1 * dx + 6x * dx + 4y * dx) + (4x + 2y + 2) * dy = 0 Reorder the terms: (1dx + 4dxy + 6dx2) + (4x + 2y + 2) * dy = 0 (1dx + 4dxy + 6dx2) + (4x + 2y + 2) * dy = 0 Reorder the terms: 1dx + 4dxy + 6dx2 + (2 + 4x + 2y) * dy = 0 Reorder the terms for easier multiplication: 1dx + 4dxy + 6dx2 + dy(2 + 4x + 2y) = 0 1dx + 4dxy + 6dx2 + (2 * dy + 4x * dy + 2y * dy) = 0 Reorder the terms: 1dx + 4dxy + 6dx2 + (4dxy + 2dy + 2dy2) = 0 1dx + 4dxy + 6dx2 + (4dxy + 2dy + 2dy2) = 0 Reorder the terms: 1dx + 4dxy + 4dxy + 6dx2 + 2dy + 2dy2 = 0 Combine like terms: 4dxy + 4dxy = 8dxy 1dx + 8dxy + 6dx2 + 2dy + 2dy2 = 0 Solving 1dx + 8dxy + 6dx2 + 2dy + 2dy2 = 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(x + 8xy + 6x2 + 2y + 2y2) = 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 '(x + 8xy + 6x2 + 2y + 2y2)' equal to zero and attempt to solve: Simplifying x + 8xy + 6x2 + 2y + 2y2 = 0 Solving x + 8xy + 6x2 + 2y + 2y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + 8xy + 6x2 + 2y + -1x + 2y2 = 0 + -1x Reorder the terms: x + -1x + 8xy + 6x2 + 2y + 2y2 = 0 + -1x Combine like terms: x + -1x = 0 0 + 8xy + 6x2 + 2y + 2y2 = 0 + -1x 8xy + 6x2 + 2y + 2y2 = 0 + -1x Remove the zero: 8xy + 6x2 + 2y + 2y2 = -1x Add '-8xy' to each side of the equation. 8xy + 6x2 + 2y + -8xy + 2y2 = -1x + -8xy Reorder the terms: 8xy + -8xy + 6x2 + 2y + 2y2 = -1x + -8xy Combine like terms: 8xy + -8xy = 0 0 + 6x2 + 2y + 2y2 = -1x + -8xy 6x2 + 2y + 2y2 = -1x + -8xy Add '-6x2' to each side of the equation. 6x2 + 2y + -6x2 + 2y2 = -1x + -8xy + -6x2 Reorder the terms: 6x2 + -6x2 + 2y + 2y2 = -1x + -8xy + -6x2 Combine like terms: 6x2 + -6x2 = 0 0 + 2y + 2y2 = -1x + -8xy + -6x2 2y + 2y2 = -1x + -8xy + -6x2 Add '-2y' to each side of the equation. 2y + -2y + 2y2 = -1x + -8xy + -6x2 + -2y Combine like terms: 2y + -2y = 0 0 + 2y2 = -1x + -8xy + -6x2 + -2y 2y2 = -1x + -8xy + -6x2 + -2y Add '-2y2' to each side of the equation. 2y2 + -2y2 = -1x + -8xy + -6x2 + -2y + -2y2 Combine like terms: 2y2 + -2y2 = 0 0 = -1x + -8xy + -6x2 + -2y + -2y2 Simplifying 0 = -1x + -8xy + -6x2 + -2y + -2y2 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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