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Simplifying (3x2y3 + y4) * dx + (3x3y2 + y4 + 4xy3) = 0 Reorder the terms for easier multiplication: dx(3x2y3 + y4) + (3x3y2 + y4 + 4xy3) = 0 (3x2y3 * dx + y4 * dx) + (3x3y2 + y4 + 4xy3) = 0 Reorder the terms: (dxy4 + 3dx3y3) + (3x3y2 + y4 + 4xy3) = 0 (dxy4 + 3dx3y3) + (3x3y2 + y4 + 4xy3) = 0 Reorder the terms: dxy4 + 3dx3y3 + (4xy3 + 3x3y2 + y4) = 0 Remove parenthesis around (4xy3 + 3x3y2 + y4) dxy4 + 3dx3y3 + 4xy3 + 3x3y2 + y4 = 0 Solving dxy4 + 3dx3y3 + 4xy3 + 3x3y2 + y4 = 0 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-4xy3' to each side of the equation. dxy4 + 3dx3y3 + 4xy3 + 3x3y2 + -4xy3 + y4 = 0 + -4xy3 Reorder the terms: dxy4 + 3dx3y3 + 4xy3 + -4xy3 + 3x3y2 + y4 = 0 + -4xy3 Combine like terms: 4xy3 + -4xy3 = 0 dxy4 + 3dx3y3 + 0 + 3x3y2 + y4 = 0 + -4xy3 dxy4 + 3dx3y3 + 3x3y2 + y4 = 0 + -4xy3 Remove the zero: dxy4 + 3dx3y3 + 3x3y2 + y4 = -4xy3 Add '-3x3y2' to each side of the equation. dxy4 + 3dx3y3 + 3x3y2 + -3x3y2 + y4 = -4xy3 + -3x3y2 Combine like terms: 3x3y2 + -3x3y2 = 0 dxy4 + 3dx3y3 + 0 + y4 = -4xy3 + -3x3y2 dxy4 + 3dx3y3 + y4 = -4xy3 + -3x3y2 Add '-1y4' to each side of the equation. dxy4 + 3dx3y3 + y4 + -1y4 = -4xy3 + -3x3y2 + -1y4 Combine like terms: y4 + -1y4 = 0 dxy4 + 3dx3y3 + 0 = -4xy3 + -3x3y2 + -1y4 dxy4 + 3dx3y3 = -4xy3 + -3x3y2 + -1y4 Reorder the terms: dxy4 + 3dx3y3 + 4xy3 + 3x3y2 + y4 = -4xy3 + 4xy3 + -3x3y2 + 3x3y2 + -1y4 + y4 Combine like terms: -4xy3 + 4xy3 = 0 dxy4 + 3dx3y3 + 4xy3 + 3x3y2 + y4 = 0 + -3x3y2 + 3x3y2 + -1y4 + y4 dxy4 + 3dx3y3 + 4xy3 + 3x3y2 + y4 = -3x3y2 + 3x3y2 + -1y4 + y4 Combine like terms: -3x3y2 + 3x3y2 = 0 dxy4 + 3dx3y3 + 4xy3 + 3x3y2 + y4 = 0 + -1y4 + y4 dxy4 + 3dx3y3 + 4xy3 + 3x3y2 + y4 = -1y4 + y4 Combine like terms: -1y4 + y4 = 0 dxy4 + 3dx3y3 + 4xy3 + 3x3y2 + y4 = 0 Factor out the Greatest Common Factor (GCF), 'y2'. y2(dxy2 + 3dx3y + 4xy + 3x3 + y2) = 0Subproblem 1
Set the factor 'y2' equal to zero and attempt to solve: Simplifying y2 = 0 Solving y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1y2' to each side of the equation. y2 + -1y2 = 0 + -1y2 Remove the zero: 0 = -1y2 Simplifying 0 = -1y2 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 '(dxy2 + 3dx3y + 4xy + 3x3 + y2)' equal to zero and attempt to solve: Simplifying dxy2 + 3dx3y + 4xy + 3x3 + y2 = 0 Solving dxy2 + 3dx3y + 4xy + 3x3 + y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-4xy' to each side of the equation. dxy2 + 3dx3y + 4xy + 3x3 + -4xy + y2 = 0 + -4xy Reorder the terms: dxy2 + 3dx3y + 4xy + -4xy + 3x3 + y2 = 0 + -4xy Combine like terms: 4xy + -4xy = 0 dxy2 + 3dx3y + 0 + 3x3 + y2 = 0 + -4xy dxy2 + 3dx3y + 3x3 + y2 = 0 + -4xy Remove the zero: dxy2 + 3dx3y + 3x3 + y2 = -4xy Add '-3x3' to each side of the equation. dxy2 + 3dx3y + 3x3 + -3x3 + y2 = -4xy + -3x3 Combine like terms: 3x3 + -3x3 = 0 dxy2 + 3dx3y + 0 + y2 = -4xy + -3x3 dxy2 + 3dx3y + y2 = -4xy + -3x3 Add '-1y2' to each side of the equation. dxy2 + 3dx3y + y2 + -1y2 = -4xy + -3x3 + -1y2 Combine like terms: y2 + -1y2 = 0 dxy2 + 3dx3y + 0 = -4xy + -3x3 + -1y2 dxy2 + 3dx3y = -4xy + -3x3 + -1y2 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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