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Simplifying (2xy + 3y2) * dx + -1(2xy + y2) * dy = 0 Reorder the terms for easier multiplication: dx(2xy + 3y2) + -1(2xy + y2) * dy = 0 (2xy * dx + 3y2 * dx) + -1(2xy + y2) * dy = 0 Reorder the terms: (3dxy2 + 2dx2y) + -1(2xy + y2) * dy = 0 (3dxy2 + 2dx2y) + -1(2xy + y2) * dy = 0 Reorder the terms for easier multiplication: 3dxy2 + 2dx2y + -1dy(2xy + y2) = 0 3dxy2 + 2dx2y + (2xy * -1dy + y2 * -1dy) = 0 3dxy2 + 2dx2y + (-2dxy2 + -1dy3) = 0 Reorder the terms: 3dxy2 + -2dxy2 + 2dx2y + -1dy3 = 0 Combine like terms: 3dxy2 + -2dxy2 = 1dxy2 1dxy2 + 2dx2y + -1dy3 = 0 Solving 1dxy2 + 2dx2y + -1dy3 = 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), 'dy'. dy(xy + 2x2 + -1y2) = 0 Factor a trinomial. dy((2x + -1y)(x + y)) = 0Subproblem 1
Set the factor 'dy' equal to zero and attempt to solve: Simplifying dy = 0 Solving dy = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dy = 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 '(2x + -1y)' equal to zero and attempt to solve: Simplifying 2x + -1y = 0 Solving 2x + -1y = 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 + -1y = 0 + -2x Combine like terms: 2x + -2x = 0 0 + -1y = 0 + -2x -1y = 0 + -2x Remove the zero: -1y = -2x Add 'y' to each side of the equation. -1y + y = -2x + y Combine like terms: -1y + y = 0 0 = -2x + y Simplifying 0 = -2x + y 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 '(x + y)' equal to zero and attempt to solve: Simplifying 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. The solution to this equation could not be determined.
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