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Simplifying (2x + 3y) * dx + (3x + 4y) * dy = 0 Reorder the terms for easier multiplication: dx(2x + 3y) + (3x + 4y) * dy = 0 (2x * dx + 3y * dx) + (3x + 4y) * dy = 0 Reorder the terms: (3dxy + 2dx2) + (3x + 4y) * dy = 0 (3dxy + 2dx2) + (3x + 4y) * dy = 0 Reorder the terms for easier multiplication: 3dxy + 2dx2 + dy(3x + 4y) = 0 3dxy + 2dx2 + (3x * dy + 4y * dy) = 0 3dxy + 2dx2 + (3dxy + 4dy2) = 0 Reorder the terms: 3dxy + 3dxy + 2dx2 + 4dy2 = 0 Combine like terms: 3dxy + 3dxy = 6dxy 6dxy + 2dx2 + 4dy2 = 0 Solving 6dxy + 2dx2 + 4dy2 = 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), '2d'. 2d(3xy + x2 + 2y2) = 0 Factor a trinomial. 2d((x + y)(x + 2y)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'd' equal to zero and attempt to solve: Simplifying d = 0 Solving d = 0 Move all terms containing d to the left, all other terms to the right. Simplifying d = 0Subproblem 2
Set the factor '(x + y)' equal to zero and attempt to solve: Simplifying x + y = 0 Solving x + y = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x + y = 0 + -1x Combine like terms: x + -1x = 0 0 + y = 0 + -1x y = 0 + -1x Remove the zero: y = -1x Add '-1y' to each side of the equation. y + -1y = -1x + -1y Combine like terms: y + -1y = 0 0 = -1x + -1y Simplifying 0 = -1x + -1y 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 '(x + 2y)' equal to zero and attempt to solve: Simplifying x + 2y = 0 Solving x + 2y = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x + 2y = 0 + -1x Combine like terms: x + -1x = 0 0 + 2y = 0 + -1x 2y = 0 + -1x Remove the zero: 2y = -1x Add '-2y' to each side of the equation. 2y + -2y = -1x + -2y Combine like terms: 2y + -2y = 0 0 = -1x + -2y Simplifying 0 = -1x + -2y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
d = {0}
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