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Simplifying (3y4 + -9x2y2 + -20x4) * dx + -1(4xy3) * dy = 0 Reorder the terms: (-9x2y2 + -20x4 + 3y4) * dx + -1(4xy3) * dy = 0 Reorder the terms for easier multiplication: dx(-9x2y2 + -20x4 + 3y4) + -1(4xy3) * dy = 0 (-9x2y2 * dx + -20x4 * dx + 3y4 * dx) + -1(4xy3) * dy = 0 Reorder the terms: (3dxy4 + -9dx3y2 + -20dx5) + -1(4xy3) * dy = 0 (3dxy4 + -9dx3y2 + -20dx5) + -1(4xy3) * dy = 0 Remove parenthesis around (4xy3) 3dxy4 + -9dx3y2 + -20dx5 + -1 * 4xy3 * dy = 0 Multiply -1 * 4 3dxy4 + -9dx3y2 + -20dx5 + -4xy3 * dy = 0 Multiply xy3 * dy 3dxy4 + -9dx3y2 + -20dx5 + -4dxy4 = 0 Reorder the terms: 3dxy4 + -4dxy4 + -9dx3y2 + -20dx5 = 0 Combine like terms: 3dxy4 + -4dxy4 = -1dxy4 -1dxy4 + -9dx3y2 + -20dx5 = 0 Solving -1dxy4 + -9dx3y2 + -20dx5 = 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), '-1dx'. -1dx(y4 + 9x2y2 + 20x4) = 0 Factor a trinomial. -1dx((y2 + 4x2)(y2 + 5x2)) = 0 Ignore the factor -1.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 '(y2 + 4x2)' equal to zero and attempt to solve: Simplifying y2 + 4x2 = 0 Reorder the terms: 4x2 + y2 = 0 Solving 4x2 + y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-4x2' to each side of the equation. 4x2 + -4x2 + y2 = 0 + -4x2 Combine like terms: 4x2 + -4x2 = 0 0 + y2 = 0 + -4x2 y2 = 0 + -4x2 Remove the zero: y2 = -4x2 Add '-1y2' to each side of the equation. y2 + -1y2 = -4x2 + -1y2 Combine like terms: y2 + -1y2 = 0 0 = -4x2 + -1y2 Simplifying 0 = -4x2 + -1y2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(y2 + 5x2)' equal to zero and attempt to solve: Simplifying y2 + 5x2 = 0 Reorder the terms: 5x2 + y2 = 0 Solving 5x2 + y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-5x2' to each side of the equation. 5x2 + -5x2 + y2 = 0 + -5x2 Combine like terms: 5x2 + -5x2 = 0 0 + y2 = 0 + -5x2 y2 = 0 + -5x2 Remove the zero: y2 = -5x2 Add '-1y2' to each side of the equation. y2 + -1y2 = -5x2 + -1y2 Combine like terms: y2 + -1y2 = 0 0 = -5x2 + -1y2 Simplifying 0 = -5x2 + -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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