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