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Simplifying (5x2y + 6x3y2 + 4xy2) * dx + (2x3 + 3x4y + 3x2y) * dy = 0 Reorder the terms: (4xy2 + 5x2y + 6x3y2) * dx + (2x3 + 3x4y + 3x2y) * dy = 0 Reorder the terms for easier multiplication: dx(4xy2 + 5x2y + 6x3y2) + (2x3 + 3x4y + 3x2y) * dy = 0 (4xy2 * dx + 5x2y * dx + 6x3y2 * dx) + (2x3 + 3x4y + 3x2y) * dy = 0 (4dx2y2 + 5dx3y + 6dx4y2) + (2x3 + 3x4y + 3x2y) * dy = 0 Reorder the terms: 4dx2y2 + 5dx3y + 6dx4y2 + (3x2y + 2x3 + 3x4y) * dy = 0 Reorder the terms for easier multiplication: 4dx2y2 + 5dx3y + 6dx4y2 + dy(3x2y + 2x3 + 3x4y) = 0 4dx2y2 + 5dx3y + 6dx4y2 + (3x2y * dy + 2x3 * dy + 3x4y * dy) = 0 4dx2y2 + 5dx3y + 6dx4y2 + (3dx2y2 + 2dx3y + 3dx4y2) = 0 Reorder the terms: 4dx2y2 + 3dx2y2 + 5dx3y + 2dx3y + 6dx4y2 + 3dx4y2 = 0 Combine like terms: 4dx2y2 + 3dx2y2 = 7dx2y2 7dx2y2 + 5dx3y + 2dx3y + 6dx4y2 + 3dx4y2 = 0 Combine like terms: 5dx3y + 2dx3y = 7dx3y 7dx2y2 + 7dx3y + 6dx4y2 + 3dx4y2 = 0 Combine like terms: 6dx4y2 + 3dx4y2 = 9dx4y2 7dx2y2 + 7dx3y + 9dx4y2 = 0 Solving 7dx2y2 + 7dx3y + 9dx4y2 = 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), 'dx2y'. dx2y(7y + 7x + 9x2y) = 0Subproblem 1
Set the factor 'dx2y' equal to zero and attempt to solve: Simplifying dx2y = 0 Solving dx2y = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dx2y = 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 '(7y + 7x + 9x2y)' equal to zero and attempt to solve: Simplifying 7y + 7x + 9x2y = 0 Reorder the terms: 7x + 9x2y + 7y = 0 Solving 7x + 9x2y + 7y = 0 Move all terms containing d to the left, all other terms to the right. Add '-7x' to each side of the equation. 7x + 9x2y + -7x + 7y = 0 + -7x Reorder the terms: 7x + -7x + 9x2y + 7y = 0 + -7x Combine like terms: 7x + -7x = 0 0 + 9x2y + 7y = 0 + -7x 9x2y + 7y = 0 + -7x Remove the zero: 9x2y + 7y = -7x Add '-9x2y' to each side of the equation. 9x2y + -9x2y + 7y = -7x + -9x2y Combine like terms: 9x2y + -9x2y = 0 0 + 7y = -7x + -9x2y 7y = -7x + -9x2y Add '-7y' to each side of the equation. 7y + -7y = -7x + -9x2y + -7y Combine like terms: 7y + -7y = 0 0 = -7x + -9x2y + -7y Simplifying 0 = -7x + -9x2y + -7y 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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