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Simplifying (2xy + y4) * dx + (3x2 + 6xy2) * dy = 0 Reorder the terms for easier multiplication: dx(2xy + y4) + (3x2 + 6xy2) * dy = 0 (2xy * dx + y4 * dx) + (3x2 + 6xy2) * dy = 0 Reorder the terms: (dxy4 + 2dx2y) + (3x2 + 6xy2) * dy = 0 (dxy4 + 2dx2y) + (3x2 + 6xy2) * dy = 0 Reorder the terms: dxy4 + 2dx2y + (6xy2 + 3x2) * dy = 0 Reorder the terms for easier multiplication: dxy4 + 2dx2y + dy(6xy2 + 3x2) = 0 dxy4 + 2dx2y + (6xy2 * dy + 3x2 * dy) = 0 dxy4 + 2dx2y + (6dxy3 + 3dx2y) = 0 Reorder the terms: 6dxy3 + dxy4 + 2dx2y + 3dx2y = 0 Combine like terms: 2dx2y + 3dx2y = 5dx2y 6dxy3 + dxy4 + 5dx2y = 0 Solving 6dxy3 + dxy4 + 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), 'dxy'. dxy(6y2 + y3 + 5x) = 0Subproblem 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 '(6y2 + y3 + 5x)' equal to zero and attempt to solve: Simplifying 6y2 + y3 + 5x = 0 Reorder the terms: 5x + 6y2 + y3 = 0 Solving 5x + 6y2 + y3 = 0 Move all terms containing d to the left, all other terms to the right. Add '-5x' to each side of the equation. 5x + 6y2 + -5x + y3 = 0 + -5x Reorder the terms: 5x + -5x + 6y2 + y3 = 0 + -5x Combine like terms: 5x + -5x = 0 0 + 6y2 + y3 = 0 + -5x 6y2 + y3 = 0 + -5x Remove the zero: 6y2 + y3 = -5x Add '-6y2' to each side of the equation. 6y2 + -6y2 + y3 = -5x + -6y2 Combine like terms: 6y2 + -6y2 = 0 0 + y3 = -5x + -6y2 y3 = -5x + -6y2 Add '-1y3' to each side of the equation. y3 + -1y3 = -5x + -6y2 + -1y3 Combine like terms: y3 + -1y3 = 0 0 = -5x + -6y2 + -1y3 Simplifying 0 = -5x + -6y2 + -1y3 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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