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Simplifying (y3 + 10xy3 + -2x) * dx + (3xy2 + 20x2y2) * dy = 0 Reorder the terms: (-2x + 10xy3 + y3) * dx + (3xy2 + 20x2y2) * dy = 0 Reorder the terms for easier multiplication: dx(-2x + 10xy3 + y3) + (3xy2 + 20x2y2) * dy = 0 (-2x * dx + 10xy3 * dx + y3 * dx) + (3xy2 + 20x2y2) * dy = 0 Reorder the terms: (dxy3 + -2dx2 + 10dx2y3) + (3xy2 + 20x2y2) * dy = 0 (dxy3 + -2dx2 + 10dx2y3) + (3xy2 + 20x2y2) * dy = 0 Reorder the terms for easier multiplication: dxy3 + -2dx2 + 10dx2y3 + dy(3xy2 + 20x2y2) = 0 dxy3 + -2dx2 + 10dx2y3 + (3xy2 * dy + 20x2y2 * dy) = 0 dxy3 + -2dx2 + 10dx2y3 + (3dxy3 + 20dx2y3) = 0 Reorder the terms: dxy3 + 3dxy3 + -2dx2 + 10dx2y3 + 20dx2y3 = 0 Combine like terms: dxy3 + 3dxy3 = 4dxy3 4dxy3 + -2dx2 + 10dx2y3 + 20dx2y3 = 0 Combine like terms: 10dx2y3 + 20dx2y3 = 30dx2y3 4dxy3 + -2dx2 + 30dx2y3 = 0 Solving 4dxy3 + -2dx2 + 30dx2y3 = 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), '2dx'. 2dx(2y3 + -1x + 15xy3) = 0 Ignore the factor 2.Subproblem 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 '(2y3 + -1x + 15xy3)' equal to zero and attempt to solve: Simplifying 2y3 + -1x + 15xy3 = 0 Reorder the terms: -1x + 15xy3 + 2y3 = 0 Solving -1x + 15xy3 + 2y3 = 0 Move all terms containing d to the left, all other terms to the right. Add 'x' to each side of the equation. -1x + 15xy3 + x + 2y3 = 0 + x Reorder the terms: -1x + x + 15xy3 + 2y3 = 0 + x Combine like terms: -1x + x = 0 0 + 15xy3 + 2y3 = 0 + x 15xy3 + 2y3 = 0 + x Remove the zero: 15xy3 + 2y3 = x Add '-15xy3' to each side of the equation. 15xy3 + -15xy3 + 2y3 = x + -15xy3 Combine like terms: 15xy3 + -15xy3 = 0 0 + 2y3 = x + -15xy3 2y3 = x + -15xy3 Add '-2y3' to each side of the equation. 2y3 + -2y3 = x + -15xy3 + -2y3 Combine like terms: 2y3 + -2y3 = 0 0 = x + -15xy3 + -2y3 Simplifying 0 = x + -15xy3 + -2y3 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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