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Simplifying (4x3y + -15x2 + -1y) * dx + (x4 + 3x2 + -1x) * dy = 0 Reorder the terms: (-15x2 + 4x3y + -1y) * dx + (x4 + 3x2 + -1x) * dy = 0 Reorder the terms for easier multiplication: dx(-15x2 + 4x3y + -1y) + (x4 + 3x2 + -1x) * dy = 0 (-15x2 * dx + 4x3y * dx + -1y * dx) + (x4 + 3x2 + -1x) * dy = 0 Reorder the terms: (-1dxy + -15dx3 + 4dx4y) + (x4 + 3x2 + -1x) * dy = 0 (-1dxy + -15dx3 + 4dx4y) + (x4 + 3x2 + -1x) * dy = 0 Reorder the terms: -1dxy + -15dx3 + 4dx4y + (-1x + 3x2 + x4) * dy = 0 Reorder the terms for easier multiplication: -1dxy + -15dx3 + 4dx4y + dy(-1x + 3x2 + x4) = 0 -1dxy + -15dx3 + 4dx4y + (-1x * dy + 3x2 * dy + x4 * dy) = 0 -1dxy + -15dx3 + 4dx4y + (-1dxy + 3dx2y + dx4y) = 0 Reorder the terms: -1dxy + -1dxy + 3dx2y + -15dx3 + 4dx4y + dx4y = 0 Combine like terms: -1dxy + -1dxy = -2dxy -2dxy + 3dx2y + -15dx3 + 4dx4y + dx4y = 0 Combine like terms: 4dx4y + dx4y = 5dx4y -2dxy + 3dx2y + -15dx3 + 5dx4y = 0 Solving -2dxy + 3dx2y + -15dx3 + 5dx4y = 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(-2y + 3xy + -15x2 + 5x3y) = 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 '(-2y + 3xy + -15x2 + 5x3y)' equal to zero and attempt to solve: Simplifying -2y + 3xy + -15x2 + 5x3y = 0 Reorder the terms: 3xy + -15x2 + 5x3y + -2y = 0 Solving 3xy + -15x2 + 5x3y + -2y = 0 Move all terms containing d to the left, all other terms to the right. Add '-3xy' to each side of the equation. 3xy + -15x2 + 5x3y + -3xy + -2y = 0 + -3xy Reorder the terms: 3xy + -3xy + -15x2 + 5x3y + -2y = 0 + -3xy Combine like terms: 3xy + -3xy = 0 0 + -15x2 + 5x3y + -2y = 0 + -3xy -15x2 + 5x3y + -2y = 0 + -3xy Remove the zero: -15x2 + 5x3y + -2y = -3xy Add '15x2' to each side of the equation. -15x2 + 5x3y + 15x2 + -2y = -3xy + 15x2 Reorder the terms: -15x2 + 15x2 + 5x3y + -2y = -3xy + 15x2 Combine like terms: -15x2 + 15x2 = 0 0 + 5x3y + -2y = -3xy + 15x2 5x3y + -2y = -3xy + 15x2 Add '-5x3y' to each side of the equation. 5x3y + -5x3y + -2y = -3xy + 15x2 + -5x3y Combine like terms: 5x3y + -5x3y = 0 0 + -2y = -3xy + 15x2 + -5x3y -2y = -3xy + 15x2 + -5x3y Add '2y' to each side of the equation. -2y + 2y = -3xy + 15x2 + -5x3y + 2y Combine like terms: -2y + 2y = 0 0 = -3xy + 15x2 + -5x3y + 2y Simplifying 0 = -3xy + 15x2 + -5x3y + 2y 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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