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Simplifying (3x2y + -4xy2) * dx + (x3 + -4x2y + 12y3) * dy = 0 Reorder the terms: (-4xy2 + 3x2y) * dx + (x3 + -4x2y + 12y3) * dy = 0 Reorder the terms for easier multiplication: dx(-4xy2 + 3x2y) + (x3 + -4x2y + 12y3) * dy = 0 (-4xy2 * dx + 3x2y * dx) + (x3 + -4x2y + 12y3) * dy = 0 (-4dx2y2 + 3dx3y) + (x3 + -4x2y + 12y3) * dy = 0 Reorder the terms: -4dx2y2 + 3dx3y + (-4x2y + x3 + 12y3) * dy = 0 Reorder the terms for easier multiplication: -4dx2y2 + 3dx3y + dy(-4x2y + x3 + 12y3) = 0 -4dx2y2 + 3dx3y + (-4x2y * dy + x3 * dy + 12y3 * dy) = 0 -4dx2y2 + 3dx3y + (-4dx2y2 + dx3y + 12dy4) = 0 Reorder the terms: -4dx2y2 + -4dx2y2 + 3dx3y + dx3y + 12dy4 = 0 Combine like terms: -4dx2y2 + -4dx2y2 = -8dx2y2 -8dx2y2 + 3dx3y + dx3y + 12dy4 = 0 Combine like terms: 3dx3y + dx3y = 4dx3y -8dx2y2 + 4dx3y + 12dy4 = 0 Solving -8dx2y2 + 4dx3y + 12dy4 = 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), '4dy'. 4dy(-2x2y + x3 + 3y3) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'dy' equal to zero and attempt to solve: Simplifying dy = 0 Solving dy = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dy = 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 '(-2x2y + x3 + 3y3)' equal to zero and attempt to solve: Simplifying -2x2y + x3 + 3y3 = 0 Solving -2x2y + x3 + 3y3 = 0 Move all terms containing d to the left, all other terms to the right. Add '2x2y' to each side of the equation. -2x2y + x3 + 2x2y + 3y3 = 0 + 2x2y Reorder the terms: -2x2y + 2x2y + x3 + 3y3 = 0 + 2x2y Combine like terms: -2x2y + 2x2y = 0 0 + x3 + 3y3 = 0 + 2x2y x3 + 3y3 = 0 + 2x2y Remove the zero: x3 + 3y3 = 2x2y Add '-1x3' to each side of the equation. x3 + -1x3 + 3y3 = 2x2y + -1x3 Combine like terms: x3 + -1x3 = 0 0 + 3y3 = 2x2y + -1x3 3y3 = 2x2y + -1x3 Add '-3y3' to each side of the equation. 3y3 + -3y3 = 2x2y + -1x3 + -3y3 Combine like terms: 3y3 + -3y3 = 0 0 = 2x2y + -1x3 + -3y3 Simplifying 0 = 2x2y + -1x3 + -3y3 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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