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Simplifying (4xy + 3y2 + -1x) * dx + x(x + 2y) * dy = 0 Reorder the terms: (-1x + 4xy + 3y2) * dx + x(x + 2y) * dy = 0 Reorder the terms for easier multiplication: dx(-1x + 4xy + 3y2) + x(x + 2y) * dy = 0 (-1x * dx + 4xy * dx + 3y2 * dx) + x(x + 2y) * dy = 0 Reorder the terms: (3dxy2 + -1dx2 + 4dx2y) + x(x + 2y) * dy = 0 (3dxy2 + -1dx2 + 4dx2y) + x(x + 2y) * dy = 0 Reorder the terms for easier multiplication: 3dxy2 + -1dx2 + 4dx2y + x * dy(x + 2y) = 0 Multiply x * dy 3dxy2 + -1dx2 + 4dx2y + dxy(x + 2y) = 0 3dxy2 + -1dx2 + 4dx2y + (x * dxy + 2y * dxy) = 0 Reorder the terms: 3dxy2 + -1dx2 + 4dx2y + (2dxy2 + dx2y) = 0 3dxy2 + -1dx2 + 4dx2y + (2dxy2 + dx2y) = 0 Reorder the terms: 3dxy2 + 2dxy2 + -1dx2 + 4dx2y + dx2y = 0 Combine like terms: 3dxy2 + 2dxy2 = 5dxy2 5dxy2 + -1dx2 + 4dx2y + dx2y = 0 Combine like terms: 4dx2y + dx2y = 5dx2y 5dxy2 + -1dx2 + 5dx2y = 0 Solving 5dxy2 + -1dx2 + 5dx2y = 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(5y2 + -1x + 5xy) = 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 '(5y2 + -1x + 5xy)' equal to zero and attempt to solve: Simplifying 5y2 + -1x + 5xy = 0 Reorder the terms: -1x + 5xy + 5y2 = 0 Solving -1x + 5xy + 5y2 = 0 Move all terms containing d to the left, all other terms to the right. Add 'x' to each side of the equation. -1x + 5xy + x + 5y2 = 0 + x Reorder the terms: -1x + x + 5xy + 5y2 = 0 + x Combine like terms: -1x + x = 0 0 + 5xy + 5y2 = 0 + x 5xy + 5y2 = 0 + x Remove the zero: 5xy + 5y2 = x Add '-5xy' to each side of the equation. 5xy + -5xy + 5y2 = x + -5xy Combine like terms: 5xy + -5xy = 0 0 + 5y2 = x + -5xy 5y2 = x + -5xy Add '-5y2' to each side of the equation. 5y2 + -5y2 = x + -5xy + -5y2 Combine like terms: 5y2 + -5y2 = 0 0 = x + -5xy + -5y2 Simplifying 0 = x + -5xy + -5y2 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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