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Simplifying (4xy + 3y2 + -1x) * dx + -1(x2 + 2xy) * dy = 0 Reorder the terms: (-1x + 4xy + 3y2) * dx + -1(x2 + 2xy) * dy = 0 Reorder the terms for easier multiplication: dx(-1x + 4xy + 3y2) + -1(x2 + 2xy) * dy = 0 (-1x * dx + 4xy * dx + 3y2 * dx) + -1(x2 + 2xy) * dy = 0 Reorder the terms: (3dxy2 + -1dx2 + 4dx2y) + -1(x2 + 2xy) * dy = 0 (3dxy2 + -1dx2 + 4dx2y) + -1(x2 + 2xy) * dy = 0 Reorder the terms: 3dxy2 + -1dx2 + 4dx2y + -1(2xy + x2) * dy = 0 Reorder the terms for easier multiplication: 3dxy2 + -1dx2 + 4dx2y + -1dy(2xy + x2) = 0 3dxy2 + -1dx2 + 4dx2y + (2xy * -1dy + x2 * -1dy) = 0 3dxy2 + -1dx2 + 4dx2y + (-2dxy2 + -1dx2y) = 0 Reorder the terms: 3dxy2 + -2dxy2 + -1dx2 + 4dx2y + -1dx2y = 0 Combine like terms: 3dxy2 + -2dxy2 = 1dxy2 1dxy2 + -1dx2 + 4dx2y + -1dx2y = 0 Combine like terms: 4dx2y + -1dx2y = 3dx2y 1dxy2 + -1dx2 + 3dx2y = 0 Solving 1dxy2 + -1dx2 + 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), 'dx'. dx(y2 + -1x + 3xy) = 0Subproblem 1
Set the factor 'dx' equal to zero and attempt to solve: Simplifying dx = 0 Solving dx = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dx = 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 '(y2 + -1x + 3xy)' equal to zero and attempt to solve: Simplifying y2 + -1x + 3xy = 0 Reorder the terms: -1x + 3xy + y2 = 0 Solving -1x + 3xy + y2 = 0 Move all terms containing d to the left, all other terms to the right. Add 'x' to each side of the equation. -1x + 3xy + x + y2 = 0 + x Reorder the terms: -1x + x + 3xy + y2 = 0 + x Combine like terms: -1x + x = 0 0 + 3xy + y2 = 0 + x 3xy + y2 = 0 + x Remove the zero: 3xy + y2 = x Add '-3xy' to each side of the equation. 3xy + -3xy + y2 = x + -3xy Combine like terms: 3xy + -3xy = 0 0 + y2 = x + -3xy y2 = x + -3xy Add '-1y2' to each side of the equation. y2 + -1y2 = x + -3xy + -1y2 Combine like terms: y2 + -1y2 = 0 0 = x + -3xy + -1y2 Simplifying 0 = x + -3xy + -1y2 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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