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Simplifying (4xy3 + -9y2 + 4xy2) * dx + (3x2y2 + -6xy + 2x2y) * dy = 0 Reorder the terms: (4xy2 + 4xy3 + -9y2) * dx + (3x2y2 + -6xy + 2x2y) * dy = 0 Reorder the terms for easier multiplication: dx(4xy2 + 4xy3 + -9y2) + (3x2y2 + -6xy + 2x2y) * dy = 0 (4xy2 * dx + 4xy3 * dx + -9y2 * dx) + (3x2y2 + -6xy + 2x2y) * dy = 0 Reorder the terms: (-9dxy2 + 4dx2y2 + 4dx2y3) + (3x2y2 + -6xy + 2x2y) * dy = 0 (-9dxy2 + 4dx2y2 + 4dx2y3) + (3x2y2 + -6xy + 2x2y) * dy = 0 Reorder the terms: -9dxy2 + 4dx2y2 + 4dx2y3 + (-6xy + 2x2y + 3x2y2) * dy = 0 Reorder the terms for easier multiplication: -9dxy2 + 4dx2y2 + 4dx2y3 + dy(-6xy + 2x2y + 3x2y2) = 0 -9dxy2 + 4dx2y2 + 4dx2y3 + (-6xy * dy + 2x2y * dy + 3x2y2 * dy) = 0 -9dxy2 + 4dx2y2 + 4dx2y3 + (-6dxy2 + 2dx2y2 + 3dx2y3) = 0 Reorder the terms: -9dxy2 + -6dxy2 + 4dx2y2 + 2dx2y2 + 4dx2y3 + 3dx2y3 = 0 Combine like terms: -9dxy2 + -6dxy2 = -15dxy2 -15dxy2 + 4dx2y2 + 2dx2y2 + 4dx2y3 + 3dx2y3 = 0 Combine like terms: 4dx2y2 + 2dx2y2 = 6dx2y2 -15dxy2 + 6dx2y2 + 4dx2y3 + 3dx2y3 = 0 Combine like terms: 4dx2y3 + 3dx2y3 = 7dx2y3 -15dxy2 + 6dx2y2 + 7dx2y3 = 0 Solving -15dxy2 + 6dx2y2 + 7dx2y3 = 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), 'dxy2'. dxy2(-15 + 6x + 7xy) = 0Subproblem 1
Set the factor 'dxy2' equal to zero and attempt to solve: Simplifying dxy2 = 0 Solving dxy2 = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dxy2 = 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 '(-15 + 6x + 7xy)' equal to zero and attempt to solve: Simplifying -15 + 6x + 7xy = 0 Solving -15 + 6x + 7xy = 0 Move all terms containing d to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 6x + 15 + 7xy = 0 + 15 Reorder the terms: -15 + 15 + 6x + 7xy = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 6x + 7xy = 0 + 15 6x + 7xy = 0 + 15 Combine like terms: 0 + 15 = 15 6x + 7xy = 15 Add '-6x' to each side of the equation. 6x + -6x + 7xy = 15 + -6x Combine like terms: 6x + -6x = 0 0 + 7xy = 15 + -6x 7xy = 15 + -6x Add '-7xy' to each side of the equation. 7xy + -7xy = 15 + -6x + -7xy Combine like terms: 7xy + -7xy = 0 0 = 15 + -6x + -7xy Simplifying 0 = 15 + -6x + -7xy 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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