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Simplifying (6x2y2 + -4y4) * dx + (2x3y + -4xy3) * dy = 0 Reorder the terms for easier multiplication: dx(6x2y2 + -4y4) + (2x3y + -4xy3) * dy = 0 (6x2y2 * dx + -4y4 * dx) + (2x3y + -4xy3) * dy = 0 Reorder the terms: (-4dxy4 + 6dx3y2) + (2x3y + -4xy3) * dy = 0 (-4dxy4 + 6dx3y2) + (2x3y + -4xy3) * dy = 0 Reorder the terms: -4dxy4 + 6dx3y2 + (-4xy3 + 2x3y) * dy = 0 Reorder the terms for easier multiplication: -4dxy4 + 6dx3y2 + dy(-4xy3 + 2x3y) = 0 -4dxy4 + 6dx3y2 + (-4xy3 * dy + 2x3y * dy) = 0 -4dxy4 + 6dx3y2 + (-4dxy4 + 2dx3y2) = 0 Reorder the terms: -4dxy4 + -4dxy4 + 6dx3y2 + 2dx3y2 = 0 Combine like terms: -4dxy4 + -4dxy4 = -8dxy4 -8dxy4 + 6dx3y2 + 2dx3y2 = 0 Combine like terms: 6dx3y2 + 2dx3y2 = 8dx3y2 -8dxy4 + 8dx3y2 = 0 Solving -8dxy4 + 8dx3y2 = 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), '8dxy2'. 8dxy2(-1y2 + x2) = 0 Factor a difference between two squares. 8dxy2((y + x)(-1y + x)) = 0 Ignore the factor 8.Subproblem 1
Set the factor 'dxy2' equal to zero and attempt to solve: Simplifying dxy2 = 0 Solving dxy2 = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dxy2 = 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 + x)' equal to zero and attempt to solve: Simplifying y + x = 0 Reorder the terms: x + y = 0 Solving x + y = 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 + y = 0 + -1x Combine like terms: x + -1x = 0 0 + y = 0 + -1x y = 0 + -1x Remove the zero: y = -1x Add '-1y' to each side of the equation. y + -1y = -1x + -1y Combine like terms: y + -1y = 0 0 = -1x + -1y Simplifying 0 = -1x + -1y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(-1y + x)' equal to zero and attempt to solve: Simplifying -1y + x = 0 Reorder the terms: x + -1y = 0 Solving x + -1y = 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 + -1y = 0 + -1x Combine like terms: x + -1x = 0 0 + -1y = 0 + -1x -1y = 0 + -1x Remove the zero: -1y = -1x Add 'y' to each side of the equation. -1y + y = -1x + y Combine like terms: -1y + y = 0 0 = -1x + y Simplifying 0 = -1x + y 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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