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Simplifying (6xy + -3y2 + 2y) * dx + 2(x + -1y) * dy = 0 Reorder the terms: (6xy + 2y + -3y2) * dx + 2(x + -1y) * dy = 0 Reorder the terms for easier multiplication: dx(6xy + 2y + -3y2) + 2(x + -1y) * dy = 0 (6xy * dx + 2y * dx + -3y2 * dx) + 2(x + -1y) * dy = 0 Reorder the terms: (2dxy + -3dxy2 + 6dx2y) + 2(x + -1y) * dy = 0 (2dxy + -3dxy2 + 6dx2y) + 2(x + -1y) * dy = 0 Reorder the terms for easier multiplication: 2dxy + -3dxy2 + 6dx2y + 2dy(x + -1y) = 0 2dxy + -3dxy2 + 6dx2y + (x * 2dy + -1y * 2dy) = 0 2dxy + -3dxy2 + 6dx2y + (2dxy + -2dy2) = 0 Reorder the terms: 2dxy + 2dxy + -3dxy2 + 6dx2y + -2dy2 = 0 Combine like terms: 2dxy + 2dxy = 4dxy 4dxy + -3dxy2 + 6dx2y + -2dy2 = 0 Solving 4dxy + -3dxy2 + 6dx2y + -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), 'dy'. dy(4x + -3xy + 6x2 + -2y) = 0Subproblem 1
Set the factor 'dy' equal to zero and attempt to solve: Simplifying dy = 0 Solving dy = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dy = 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 '(4x + -3xy + 6x2 + -2y)' equal to zero and attempt to solve: Simplifying 4x + -3xy + 6x2 + -2y = 0 Solving 4x + -3xy + 6x2 + -2y = 0 Move all terms containing d to the left, all other terms to the right. Add '-4x' to each side of the equation. 4x + -3xy + 6x2 + -4x + -2y = 0 + -4x Reorder the terms: 4x + -4x + -3xy + 6x2 + -2y = 0 + -4x Combine like terms: 4x + -4x = 0 0 + -3xy + 6x2 + -2y = 0 + -4x -3xy + 6x2 + -2y = 0 + -4x Remove the zero: -3xy + 6x2 + -2y = -4x Add '3xy' to each side of the equation. -3xy + 6x2 + 3xy + -2y = -4x + 3xy Reorder the terms: -3xy + 3xy + 6x2 + -2y = -4x + 3xy Combine like terms: -3xy + 3xy = 0 0 + 6x2 + -2y = -4x + 3xy 6x2 + -2y = -4x + 3xy Add '-6x2' to each side of the equation. 6x2 + -6x2 + -2y = -4x + 3xy + -6x2 Combine like terms: 6x2 + -6x2 = 0 0 + -2y = -4x + 3xy + -6x2 -2y = -4x + 3xy + -6x2 Add '2y' to each side of the equation. -2y + 2y = -4x + 3xy + -6x2 + 2y Combine like terms: -2y + 2y = 0 0 = -4x + 3xy + -6x2 + 2y Simplifying 0 = -4x + 3xy + -6x2 + 2y 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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