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