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Simplifying (2y2 + 3xy + -2y + 6x) * dx + x(x + 2y + -1) * dy = 0 Reorder the terms: (6x + 3xy + -2y + 2y2) * dx + x(x + 2y + -1) * dy = 0 Reorder the terms for easier multiplication: dx(6x + 3xy + -2y + 2y2) + x(x + 2y + -1) * dy = 0 (6x * dx + 3xy * dx + -2y * dx + 2y2 * dx) + x(x + 2y + -1) * dy = 0 Reorder the terms: (-2dxy + 2dxy2 + 6dx2 + 3dx2y) + x(x + 2y + -1) * dy = 0 (-2dxy + 2dxy2 + 6dx2 + 3dx2y) + x(x + 2y + -1) * dy = 0 Reorder the terms: -2dxy + 2dxy2 + 6dx2 + 3dx2y + x(-1 + x + 2y) * dy = 0 Reorder the terms for easier multiplication: -2dxy + 2dxy2 + 6dx2 + 3dx2y + x * dy(-1 + x + 2y) = 0 Multiply x * dy -2dxy + 2dxy2 + 6dx2 + 3dx2y + dxy(-1 + x + 2y) = 0 -2dxy + 2dxy2 + 6dx2 + 3dx2y + (-1 * dxy + x * dxy + 2y * dxy) = 0 Reorder the terms: -2dxy + 2dxy2 + 6dx2 + 3dx2y + (-1dxy + 2dxy2 + dx2y) = 0 -2dxy + 2dxy2 + 6dx2 + 3dx2y + (-1dxy + 2dxy2 + dx2y) = 0 Reorder the terms: -2dxy + -1dxy + 2dxy2 + 2dxy2 + 6dx2 + 3dx2y + dx2y = 0 Combine like terms: -2dxy + -1dxy = -3dxy -3dxy + 2dxy2 + 2dxy2 + 6dx2 + 3dx2y + dx2y = 0 Combine like terms: 2dxy2 + 2dxy2 = 4dxy2 -3dxy + 4dxy2 + 6dx2 + 3dx2y + dx2y = 0 Combine like terms: 3dx2y + dx2y = 4dx2y -3dxy + 4dxy2 + 6dx2 + 4dx2y = 0 Solving -3dxy + 4dxy2 + 6dx2 + 4dx2y = 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), 'dx'. dx(-3y + 4y2 + 6x + 4xy) = 0Subproblem 1
Set the factor 'dx' equal to zero and attempt to solve: Simplifying dx = 0 Solving dx = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dx = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-3y + 4y2 + 6x + 4xy)' equal to zero and attempt to solve: Simplifying -3y + 4y2 + 6x + 4xy = 0 Reorder the terms: 6x + 4xy + -3y + 4y2 = 0 Solving 6x + 4xy + -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 + 4xy + -3y + -6x + 4y2 = 0 + -6x Reorder the terms: 6x + -6x + 4xy + -3y + 4y2 = 0 + -6x Combine like terms: 6x + -6x = 0 0 + 4xy + -3y + 4y2 = 0 + -6x 4xy + -3y + 4y2 = 0 + -6x Remove the zero: 4xy + -3y + 4y2 = -6x Add '-4xy' to each side of the equation. 4xy + -3y + -4xy + 4y2 = -6x + -4xy Reorder the terms: 4xy + -4xy + -3y + 4y2 = -6x + -4xy Combine like terms: 4xy + -4xy = 0 0 + -3y + 4y2 = -6x + -4xy -3y + 4y2 = -6x + -4xy Add '3y' to each side of the equation. -3y + 3y + 4y2 = -6x + -4xy + 3y Combine like terms: -3y + 3y = 0 0 + 4y2 = -6x + -4xy + 3y 4y2 = -6x + -4xy + 3y Add '-4y2' to each side of the equation. 4y2 + -4y2 = -6x + -4xy + 3y + -4y2 Combine like terms: 4y2 + -4y2 = 0 0 = -6x + -4xy + 3y + -4y2 Simplifying 0 = -6x + -4xy + 3y + -4y2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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