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Simplifying (3x + y2 + 2y5) * dx + (2x2y + 5xy4) * dy = 0 Reorder the terms for easier multiplication: dx(3x + y2 + 2y5) + (2x2y + 5xy4) * dy = 0 (3x * dx + y2 * dx + 2y5 * dx) + (2x2y + 5xy4) * dy = 0 Reorder the terms: (dxy2 + 2dxy5 + 3dx2) + (2x2y + 5xy4) * dy = 0 (dxy2 + 2dxy5 + 3dx2) + (2x2y + 5xy4) * dy = 0 Reorder the terms: dxy2 + 2dxy5 + 3dx2 + (5xy4 + 2x2y) * dy = 0 Reorder the terms for easier multiplication: dxy2 + 2dxy5 + 3dx2 + dy(5xy4 + 2x2y) = 0 dxy2 + 2dxy5 + 3dx2 + (5xy4 * dy + 2x2y * dy) = 0 dxy2 + 2dxy5 + 3dx2 + (5dxy5 + 2dx2y2) = 0 Reorder the terms: dxy2 + 2dxy5 + 5dxy5 + 3dx2 + 2dx2y2 = 0 Combine like terms: 2dxy5 + 5dxy5 = 7dxy5 dxy2 + 7dxy5 + 3dx2 + 2dx2y2 = 0 Solving dxy2 + 7dxy5 + 3dx2 + 2dx2y2 = 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(y2 + 7y5 + 3x + 2xy2) = 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 '(y2 + 7y5 + 3x + 2xy2)' equal to zero and attempt to solve: Simplifying y2 + 7y5 + 3x + 2xy2 = 0 Reorder the terms: 3x + 2xy2 + y2 + 7y5 = 0 Solving 3x + 2xy2 + y2 + 7y5 = 0 Move all terms containing d to the left, all other terms to the right. Add '-3x' to each side of the equation. 3x + 2xy2 + y2 + -3x + 7y5 = 0 + -3x Reorder the terms: 3x + -3x + 2xy2 + y2 + 7y5 = 0 + -3x Combine like terms: 3x + -3x = 0 0 + 2xy2 + y2 + 7y5 = 0 + -3x 2xy2 + y2 + 7y5 = 0 + -3x Remove the zero: 2xy2 + y2 + 7y5 = -3x Add '-2xy2' to each side of the equation. 2xy2 + y2 + -2xy2 + 7y5 = -3x + -2xy2 Reorder the terms: 2xy2 + -2xy2 + y2 + 7y5 = -3x + -2xy2 Combine like terms: 2xy2 + -2xy2 = 0 0 + y2 + 7y5 = -3x + -2xy2 y2 + 7y5 = -3x + -2xy2 Add '-1y2' to each side of the equation. y2 + -1y2 + 7y5 = -3x + -2xy2 + -1y2 Combine like terms: y2 + -1y2 = 0 0 + 7y5 = -3x + -2xy2 + -1y2 7y5 = -3x + -2xy2 + -1y2 Add '-7y5' to each side of the equation. 7y5 + -7y5 = -3x + -2xy2 + -1y2 + -7y5 Combine like terms: 7y5 + -7y5 = 0 0 = -3x + -2xy2 + -1y2 + -7y5 Simplifying 0 = -3x + -2xy2 + -1y2 + -7y5 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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