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Simplifying 2y(x + -1y) * dx + x(x + -4y) * dy = 0 Reorder the terms for easier multiplication: 2y * dx(x + -1y) + x(x + -4y) * dy = 0 Multiply y * dx 2dxy(x + -1y) + x(x + -4y) * dy = 0 (x * 2dxy + -1y * 2dxy) + x(x + -4y) * dy = 0 Reorder the terms: (-2dxy2 + 2dx2y) + x(x + -4y) * dy = 0 (-2dxy2 + 2dx2y) + x(x + -4y) * dy = 0 Reorder the terms for easier multiplication: -2dxy2 + 2dx2y + x * dy(x + -4y) = 0 Multiply x * dy -2dxy2 + 2dx2y + dxy(x + -4y) = 0 -2dxy2 + 2dx2y + (x * dxy + -4y * dxy) = 0 Reorder the terms: -2dxy2 + 2dx2y + (-4dxy2 + dx2y) = 0 -2dxy2 + 2dx2y + (-4dxy2 + dx2y) = 0 Reorder the terms: -2dxy2 + -4dxy2 + 2dx2y + dx2y = 0 Combine like terms: -2dxy2 + -4dxy2 = -6dxy2 -6dxy2 + 2dx2y + dx2y = 0 Combine like terms: 2dx2y + dx2y = 3dx2y -6dxy2 + 3dx2y = 0 Solving -6dxy2 + 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(-2y + 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 '(-2y + x)' equal to zero and attempt to solve: Simplifying -2y + x = 0 Reorder the terms: x + -2y = 0 Solving x + -2y = 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 + -2y = 0 + -1x Combine like terms: x + -1x = 0 0 + -2y = 0 + -1x -2y = 0 + -1x Remove the zero: -2y = -1x Add '2y' to each side of the equation. -2y + 2y = -1x + 2y Combine like terms: -2y + 2y = 0 0 = -1x + 2y Simplifying 0 = -1x + 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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