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Simplifying (2xy3 + -2x3y3 + -4xy2 + 2x) * dx + (3x2y2 + 4y) * dy = 0 Reorder the terms: (2x + -4xy2 + 2xy3 + -2x3y3) * dx + (3x2y2 + 4y) * dy = 0 Reorder the terms for easier multiplication: dx(2x + -4xy2 + 2xy3 + -2x3y3) + (3x2y2 + 4y) * dy = 0 (2x * dx + -4xy2 * dx + 2xy3 * dx + -2x3y3 * dx) + (3x2y2 + 4y) * dy = 0 (2dx2 + -4dx2y2 + 2dx2y3 + -2dx4y3) + (3x2y2 + 4y) * dy = 0 Reorder the terms for easier multiplication: 2dx2 + -4dx2y2 + 2dx2y3 + -2dx4y3 + dy(3x2y2 + 4y) = 0 2dx2 + -4dx2y2 + 2dx2y3 + -2dx4y3 + (3x2y2 * dy + 4y * dy) = 0 2dx2 + -4dx2y2 + 2dx2y3 + -2dx4y3 + (3dx2y3 + 4dy2) = 0 Reorder the terms: 2dx2 + -4dx2y2 + 2dx2y3 + 3dx2y3 + -2dx4y3 + 4dy2 = 0 Combine like terms: 2dx2y3 + 3dx2y3 = 5dx2y3 2dx2 + -4dx2y2 + 5dx2y3 + -2dx4y3 + 4dy2 = 0 Solving 2dx2 + -4dx2y2 + 5dx2y3 + -2dx4y3 + 4dy2 = 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), 'd'. d(2x2 + -4x2y2 + 5x2y3 + -2x4y3 + 4y2) = 0Subproblem 1
Set the factor 'd' equal to zero and attempt to solve: Simplifying d = 0 Solving d = 0 Move all terms containing d to the left, all other terms to the right. Simplifying d = 0Subproblem 2
Set the factor '(2x2 + -4x2y2 + 5x2y3 + -2x4y3 + 4y2)' equal to zero and attempt to solve: Simplifying 2x2 + -4x2y2 + 5x2y3 + -2x4y3 + 4y2 = 0 Solving 2x2 + -4x2y2 + 5x2y3 + -2x4y3 + 4y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-2x2' to each side of the equation. 2x2 + -4x2y2 + 5x2y3 + -2x4y3 + -2x2 + 4y2 = 0 + -2x2 Reorder the terms: 2x2 + -2x2 + -4x2y2 + 5x2y3 + -2x4y3 + 4y2 = 0 + -2x2 Combine like terms: 2x2 + -2x2 = 0 0 + -4x2y2 + 5x2y3 + -2x4y3 + 4y2 = 0 + -2x2 -4x2y2 + 5x2y3 + -2x4y3 + 4y2 = 0 + -2x2 Remove the zero: -4x2y2 + 5x2y3 + -2x4y3 + 4y2 = -2x2 Add '4x2y2' to each side of the equation. -4x2y2 + 5x2y3 + -2x4y3 + 4x2y2 + 4y2 = -2x2 + 4x2y2 Reorder the terms: -4x2y2 + 4x2y2 + 5x2y3 + -2x4y3 + 4y2 = -2x2 + 4x2y2 Combine like terms: -4x2y2 + 4x2y2 = 0 0 + 5x2y3 + -2x4y3 + 4y2 = -2x2 + 4x2y2 5x2y3 + -2x4y3 + 4y2 = -2x2 + 4x2y2 Add '-5x2y3' to each side of the equation. 5x2y3 + -2x4y3 + -5x2y3 + 4y2 = -2x2 + 4x2y2 + -5x2y3 Reorder the terms: 5x2y3 + -5x2y3 + -2x4y3 + 4y2 = -2x2 + 4x2y2 + -5x2y3 Combine like terms: 5x2y3 + -5x2y3 = 0 0 + -2x4y3 + 4y2 = -2x2 + 4x2y2 + -5x2y3 -2x4y3 + 4y2 = -2x2 + 4x2y2 + -5x2y3 Add '2x4y3' to each side of the equation. -2x4y3 + 2x4y3 + 4y2 = -2x2 + 4x2y2 + -5x2y3 + 2x4y3 Combine like terms: -2x4y3 + 2x4y3 = 0 0 + 4y2 = -2x2 + 4x2y2 + -5x2y3 + 2x4y3 4y2 = -2x2 + 4x2y2 + -5x2y3 + 2x4y3 Add '-4y2' to each side of the equation. 4y2 + -4y2 = -2x2 + 4x2y2 + -5x2y3 + 2x4y3 + -4y2 Combine like terms: 4y2 + -4y2 = 0 0 = -2x2 + 4x2y2 + -5x2y3 + 2x4y3 + -4y2 Simplifying 0 = -2x2 + 4x2y2 + -5x2y3 + 2x4y3 + -4y2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
d = {0}
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