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Simplifying y(8x + -9y) * dx + 2x(x + -3y) * dy = 0 Reorder the terms for easier multiplication: y * dx(8x + -9y) + 2x(x + -3y) * dy = 0 Multiply y * dx dxy(8x + -9y) + 2x(x + -3y) * dy = 0 (8x * dxy + -9y * dxy) + 2x(x + -3y) * dy = 0 Reorder the terms: (-9dxy2 + 8dx2y) + 2x(x + -3y) * dy = 0 (-9dxy2 + 8dx2y) + 2x(x + -3y) * dy = 0 Reorder the terms for easier multiplication: -9dxy2 + 8dx2y + 2x * dy(x + -3y) = 0 Multiply x * dy -9dxy2 + 8dx2y + 2dxy(x + -3y) = 0 -9dxy2 + 8dx2y + (x * 2dxy + -3y * 2dxy) = 0 Reorder the terms: -9dxy2 + 8dx2y + (-6dxy2 + 2dx2y) = 0 -9dxy2 + 8dx2y + (-6dxy2 + 2dx2y) = 0 Reorder the terms: -9dxy2 + -6dxy2 + 8dx2y + 2dx2y = 0 Combine like terms: -9dxy2 + -6dxy2 = -15dxy2 -15dxy2 + 8dx2y + 2dx2y = 0 Combine like terms: 8dx2y + 2dx2y = 10dx2y -15dxy2 + 10dx2y = 0 Solving -15dxy2 + 10dx2y = 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), '5dxy'. 5dxy(-3y + 2x) = 0 Ignore the factor 5.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 '(-3y + 2x)' equal to zero and attempt to solve: Simplifying -3y + 2x = 0 Reorder the terms: 2x + -3y = 0 Solving 2x + -3y = 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 + -3y = 0 + -2x Combine like terms: 2x + -2x = 0 0 + -3y = 0 + -2x -3y = 0 + -2x Remove the zero: -3y = -2x Add '3y' to each side of the equation. -3y + 3y = -2x + 3y Combine like terms: -3y + 3y = 0 0 = -2x + 3y Simplifying 0 = -2x + 3y 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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