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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 for easier multiplication: dx(-1 + 4x + -6y) + (3x + -2y + -2) * dy = 0 (-1 * dx + 4x * dx + -6y * dx) + (3x + -2y + -2) * dy = 0 Reorder the terms: (-1dx + -6dxy + 4dx2) + (3x + -2y + -2) * dy = 0 (-1dx + -6dxy + 4dx2) + (3x + -2y + -2) * dy = 0 Reorder the terms: -1dx + -6dxy + 4dx2 + (-2 + 3x + -2y) * dy = 0 Reorder the terms for easier multiplication: -1dx + -6dxy + 4dx2 + dy(-2 + 3x + -2y) = 0 -1dx + -6dxy + 4dx2 + (-2 * dy + 3x * dy + -2y * dy) = 0 Reorder the terms: -1dx + -6dxy + 4dx2 + (3dxy + -2dy + -2dy2) = 0 -1dx + -6dxy + 4dx2 + (3dxy + -2dy + -2dy2) = 0 Reorder the terms: -1dx + -6dxy + 3dxy + 4dx2 + -2dy + -2dy2 = 0 Combine like terms: -6dxy + 3dxy = -3dxy -1dx + -3dxy + 4dx2 + -2dy + -2dy2 = 0 Solving -1dx + -3dxy + 4dx2 + -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(-1x + -3xy + 4x2 + -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 '(-1x + -3xy + 4x2 + -2y + -2y2)' equal to zero and attempt to solve: Simplifying -1x + -3xy + 4x2 + -2y + -2y2 = 0 Solving -1x + -3xy + 4x2 + -2y + -2y2 = 0 Move all terms containing d to the left, all other terms to the right. Add 'x' to each side of the equation. -1x + -3xy + 4x2 + -2y + x + -2y2 = 0 + x Reorder the terms: -1x + x + -3xy + 4x2 + -2y + -2y2 = 0 + x Combine like terms: -1x + x = 0 0 + -3xy + 4x2 + -2y + -2y2 = 0 + x -3xy + 4x2 + -2y + -2y2 = 0 + x Remove the zero: -3xy + 4x2 + -2y + -2y2 = x Add '3xy' to each side of the equation. -3xy + 4x2 + -2y + 3xy + -2y2 = x + 3xy Reorder the terms: -3xy + 3xy + 4x2 + -2y + -2y2 = x + 3xy Combine like terms: -3xy + 3xy = 0 0 + 4x2 + -2y + -2y2 = x + 3xy 4x2 + -2y + -2y2 = x + 3xy Add '-4x2' to each side of the equation. 4x2 + -2y + -4x2 + -2y2 = x + 3xy + -4x2 Reorder the terms: 4x2 + -4x2 + -2y + -2y2 = x + 3xy + -4x2 Combine like terms: 4x2 + -4x2 = 0 0 + -2y + -2y2 = x + 3xy + -4x2 -2y + -2y2 = x + 3xy + -4x2 Add '2y' to each side of the equation. -2y + 2y + -2y2 = x + 3xy + -4x2 + 2y Combine like terms: -2y + 2y = 0 0 + -2y2 = x + 3xy + -4x2 + 2y -2y2 = x + 3xy + -4x2 + 2y Add '2y2' to each side of the equation. -2y2 + 2y2 = x + 3xy + -4x2 + 2y + 2y2 Combine like terms: -2y2 + 2y2 = 0 0 = x + 3xy + -4x2 + 2y + 2y2 Simplifying 0 = x + 3xy + -4x2 + 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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