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