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Simplifying (6y + -3x2 + 3y2) * dx + (6x + 6xy) * dy = 0 Reorder the terms: (-3x2 + 6y + 3y2) * dx + (6x + 6xy) * dy = 0 Reorder the terms for easier multiplication: dx(-3x2 + 6y + 3y2) + (6x + 6xy) * dy = 0 (-3x2 * dx + 6y * dx + 3y2 * dx) + (6x + 6xy) * dy = 0 Reorder the terms: (6dxy + 3dxy2 + -3dx3) + (6x + 6xy) * dy = 0 (6dxy + 3dxy2 + -3dx3) + (6x + 6xy) * dy = 0 Reorder the terms for easier multiplication: 6dxy + 3dxy2 + -3dx3 + dy(6x + 6xy) = 0 6dxy + 3dxy2 + -3dx3 + (6x * dy + 6xy * dy) = 0 6dxy + 3dxy2 + -3dx3 + (6dxy + 6dxy2) = 0 Reorder the terms: 6dxy + 6dxy + 3dxy2 + 6dxy2 + -3dx3 = 0 Combine like terms: 6dxy + 6dxy = 12dxy 12dxy + 3dxy2 + 6dxy2 + -3dx3 = 0 Combine like terms: 3dxy2 + 6dxy2 = 9dxy2 12dxy + 9dxy2 + -3dx3 = 0 Solving 12dxy + 9dxy2 + -3dx3 = 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), '3dx'. 3dx(4y + 3y2 + -1x2) = 0 Ignore the factor 3.Subproblem 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 '(4y + 3y2 + -1x2)' equal to zero and attempt to solve: Simplifying 4y + 3y2 + -1x2 = 0 Reorder the terms: -1x2 + 4y + 3y2 = 0 Solving -1x2 + 4y + 3y2 = 0 Move all terms containing d to the left, all other terms to the right. Add 'x2' to each side of the equation. -1x2 + 4y + x2 + 3y2 = 0 + x2 Reorder the terms: -1x2 + x2 + 4y + 3y2 = 0 + x2 Combine like terms: -1x2 + x2 = 0 0 + 4y + 3y2 = 0 + x2 4y + 3y2 = 0 + x2 Remove the zero: 4y + 3y2 = x2 Add '-4y' to each side of the equation. 4y + -4y + 3y2 = x2 + -4y Combine like terms: 4y + -4y = 0 0 + 3y2 = x2 + -4y 3y2 = x2 + -4y Add '-3y2' to each side of the equation. 3y2 + -3y2 = x2 + -4y + -3y2 Combine like terms: 3y2 + -3y2 = 0 0 = x2 + -4y + -3y2 Simplifying 0 = x2 + -4y + -3y2 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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