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Simplifying (6xy + -1y2) * dx + (4y + 3x2) * dy = 0 Reorder the terms for easier multiplication: dx(6xy + -1y2) + (4y + 3x2) * dy = 0 (6xy * dx + -1y2 * dx) + (4y + 3x2) * dy = 0 Reorder the terms: (-1dxy2 + 6dx2y) + (4y + 3x2) * dy = 0 (-1dxy2 + 6dx2y) + (4y + 3x2) * dy = 0 Reorder the terms: -1dxy2 + 6dx2y + (3x2 + 4y) * dy = 0 Reorder the terms for easier multiplication: -1dxy2 + 6dx2y + dy(3x2 + 4y) = 0 -1dxy2 + 6dx2y + (3x2 * dy + 4y * dy) = 0 -1dxy2 + 6dx2y + (3dx2y + 4dy2) = 0 Combine like terms: 6dx2y + 3dx2y = 9dx2y -1dxy2 + 9dx2y + 4dy2 = 0 Solving -1dxy2 + 9dx2y + 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), 'dy'. dy(-1xy + 9x2 + 4y) = 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 '(-1xy + 9x2 + 4y)' equal to zero and attempt to solve: Simplifying -1xy + 9x2 + 4y = 0 Solving -1xy + 9x2 + 4y = 0 Move all terms containing d to the left, all other terms to the right. Add 'xy' to each side of the equation. -1xy + 9x2 + xy + 4y = 0 + xy Reorder the terms: -1xy + xy + 9x2 + 4y = 0 + xy Combine like terms: -1xy + xy = 0 0 + 9x2 + 4y = 0 + xy 9x2 + 4y = 0 + xy Remove the zero: 9x2 + 4y = xy Add '-9x2' to each side of the equation. 9x2 + -9x2 + 4y = xy + -9x2 Combine like terms: 9x2 + -9x2 = 0 0 + 4y = xy + -9x2 4y = xy + -9x2 Add '-4y' to each side of the equation. 4y + -4y = xy + -9x2 + -4y Combine like terms: 4y + -4y = 0 0 = xy + -9x2 + -4y Simplifying 0 = xy + -9x2 + -4y 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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