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Simplifying (4x3y3 + 3x2y2 + 2xy) * dx + (3x4y2 + 2x3y + x2) * dy = 0 Reorder the terms: (2xy + 3x2y2 + 4x3y3) * dx + (3x4y2 + 2x3y + x2) * dy = 0 Reorder the terms for easier multiplication: dx(2xy + 3x2y2 + 4x3y3) + (3x4y2 + 2x3y + x2) * dy = 0 (2xy * dx + 3x2y2 * dx + 4x3y3 * dx) + (3x4y2 + 2x3y + x2) * dy = 0 (2dx2y + 3dx3y2 + 4dx4y3) + (3x4y2 + 2x3y + x2) * dy = 0 Reorder the terms: 2dx2y + 3dx3y2 + 4dx4y3 + (x2 + 2x3y + 3x4y2) * dy = 0 Reorder the terms for easier multiplication: 2dx2y + 3dx3y2 + 4dx4y3 + dy(x2 + 2x3y + 3x4y2) = 0 2dx2y + 3dx3y2 + 4dx4y3 + (x2 * dy + 2x3y * dy + 3x4y2 * dy) = 0 2dx2y + 3dx3y2 + 4dx4y3 + (dx2y + 2dx3y2 + 3dx4y3) = 0 Reorder the terms: 2dx2y + dx2y + 3dx3y2 + 2dx3y2 + 4dx4y3 + 3dx4y3 = 0 Combine like terms: 2dx2y + dx2y = 3dx2y 3dx2y + 3dx3y2 + 2dx3y2 + 4dx4y3 + 3dx4y3 = 0 Combine like terms: 3dx3y2 + 2dx3y2 = 5dx3y2 3dx2y + 5dx3y2 + 4dx4y3 + 3dx4y3 = 0 Combine like terms: 4dx4y3 + 3dx4y3 = 7dx4y3 3dx2y + 5dx3y2 + 7dx4y3 = 0 Solving 3dx2y + 5dx3y2 + 7dx4y3 = 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), 'dx2y'. dx2y(3 + 5xy + 7x2y2) = 0Subproblem 1
Set the factor 'dx2y' equal to zero and attempt to solve: Simplifying dx2y = 0 Solving dx2y = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dx2y = 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 '(3 + 5xy + 7x2y2)' equal to zero and attempt to solve: Simplifying 3 + 5xy + 7x2y2 = 0 Solving 3 + 5xy + 7x2y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + 5xy + -3 + 7x2y2 = 0 + -3 Reorder the terms: 3 + -3 + 5xy + 7x2y2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 5xy + 7x2y2 = 0 + -3 5xy + 7x2y2 = 0 + -3 Combine like terms: 0 + -3 = -3 5xy + 7x2y2 = -3 Add '-5xy' to each side of the equation. 5xy + -5xy + 7x2y2 = -3 + -5xy Combine like terms: 5xy + -5xy = 0 0 + 7x2y2 = -3 + -5xy 7x2y2 = -3 + -5xy Add '-7x2y2' to each side of the equation. 7x2y2 + -7x2y2 = -3 + -5xy + -7x2y2 Combine like terms: 7x2y2 + -7x2y2 = 0 0 = -3 + -5xy + -7x2y2 Simplifying 0 = -3 + -5xy + -7x2y2 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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