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Simplifying y(x + -6y) * dx + x(2x + -9y) * dy = 0 Reorder the terms for easier multiplication: y * dx(x + -6y) + x(2x + -9y) * dy = 0 Multiply y * dx dxy(x + -6y) + x(2x + -9y) * dy = 0 (x * dxy + -6y * dxy) + x(2x + -9y) * dy = 0 Reorder the terms: (-6dxy2 + dx2y) + x(2x + -9y) * dy = 0 (-6dxy2 + dx2y) + x(2x + -9y) * dy = 0 Reorder the terms for easier multiplication: -6dxy2 + dx2y + x * dy(2x + -9y) = 0 Multiply x * dy -6dxy2 + dx2y + dxy(2x + -9y) = 0 -6dxy2 + dx2y + (2x * dxy + -9y * dxy) = 0 Reorder the terms: -6dxy2 + dx2y + (-9dxy2 + 2dx2y) = 0 -6dxy2 + dx2y + (-9dxy2 + 2dx2y) = 0 Reorder the terms: -6dxy2 + -9dxy2 + dx2y + 2dx2y = 0 Combine like terms: -6dxy2 + -9dxy2 = -15dxy2 -15dxy2 + dx2y + 2dx2y = 0 Combine like terms: dx2y + 2dx2y = 3dx2y -15dxy2 + 3dx2y = 0 Solving -15dxy2 + 3dx2y = 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), '3dxy'. 3dxy(-5y + x) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'dxy' equal to zero and attempt to solve: Simplifying dxy = 0 Solving dxy = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dxy = 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 '(-5y + x)' equal to zero and attempt to solve: Simplifying -5y + x = 0 Reorder the terms: x + -5y = 0 Solving x + -5y = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x + -5y = 0 + -1x Combine like terms: x + -1x = 0 0 + -5y = 0 + -1x -5y = 0 + -1x Remove the zero: -5y = -1x Add '5y' to each side of the equation. -5y + 5y = -1x + 5y Combine like terms: -5y + 5y = 0 0 = -1x + 5y Simplifying 0 = -1x + 5y 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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