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Simplifying (2x + 3y + 4) * dx = (4x + 6y + 1) * dy Reorder the terms: (4 + 2x + 3y) * dx = (4x + 6y + 1) * dy Reorder the terms for easier multiplication: dx(4 + 2x + 3y) = (4x + 6y + 1) * dy (4 * dx + 2x * dx + 3y * dx) = (4x + 6y + 1) * dy Reorder the terms: (4dx + 3dxy + 2dx2) = (4x + 6y + 1) * dy (4dx + 3dxy + 2dx2) = (4x + 6y + 1) * dy Reorder the terms: 4dx + 3dxy + 2dx2 = (1 + 4x + 6y) * dy Reorder the terms for easier multiplication: 4dx + 3dxy + 2dx2 = dy(1 + 4x + 6y) 4dx + 3dxy + 2dx2 = (1 * dy + 4x * dy + 6y * dy) Reorder the terms: 4dx + 3dxy + 2dx2 = (4dxy + 1dy + 6dy2) 4dx + 3dxy + 2dx2 = (4dxy + 1dy + 6dy2) Solving 4dx + 3dxy + 2dx2 = 4dxy + 1dy + 6dy2 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-4dxy' to each side of the equation. 4dx + 3dxy + -4dxy + 2dx2 = 4dxy + 1dy + -4dxy + 6dy2 Combine like terms: 3dxy + -4dxy = -1dxy 4dx + -1dxy + 2dx2 = 4dxy + 1dy + -4dxy + 6dy2 Reorder the terms: 4dx + -1dxy + 2dx2 = 4dxy + -4dxy + 1dy + 6dy2 Combine like terms: 4dxy + -4dxy = 0 4dx + -1dxy + 2dx2 = 0 + 1dy + 6dy2 4dx + -1dxy + 2dx2 = 1dy + 6dy2 Add '-1dy' to each side of the equation. 4dx + -1dxy + 2dx2 + -1dy = 1dy + -1dy + 6dy2 Combine like terms: 1dy + -1dy = 0 4dx + -1dxy + 2dx2 + -1dy = 0 + 6dy2 4dx + -1dxy + 2dx2 + -1dy = 6dy2 Add '-6dy2' to each side of the equation. 4dx + -1dxy + 2dx2 + -1dy + -6dy2 = 6dy2 + -6dy2 Combine like terms: 6dy2 + -6dy2 = 0 4dx + -1dxy + 2dx2 + -1dy + -6dy2 = 0 Factor out the Greatest Common Factor (GCF), 'd'. d(4x + -1xy + 2x2 + -1y + -6y2) = 0Subproblem 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 '(4x + -1xy + 2x2 + -1y + -6y2)' equal to zero and attempt to solve: Simplifying 4x + -1xy + 2x2 + -1y + -6y2 = 0 Solving 4x + -1xy + 2x2 + -1y + -6y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-4x' to each side of the equation. 4x + -1xy + 2x2 + -1y + -4x + -6y2 = 0 + -4x Reorder the terms: 4x + -4x + -1xy + 2x2 + -1y + -6y2 = 0 + -4x Combine like terms: 4x + -4x = 0 0 + -1xy + 2x2 + -1y + -6y2 = 0 + -4x -1xy + 2x2 + -1y + -6y2 = 0 + -4x Remove the zero: -1xy + 2x2 + -1y + -6y2 = -4x Add 'xy' to each side of the equation. -1xy + 2x2 + -1y + xy + -6y2 = -4x + xy Reorder the terms: -1xy + xy + 2x2 + -1y + -6y2 = -4x + xy Combine like terms: -1xy + xy = 0 0 + 2x2 + -1y + -6y2 = -4x + xy 2x2 + -1y + -6y2 = -4x + xy Add '-2x2' to each side of the equation. 2x2 + -1y + -2x2 + -6y2 = -4x + xy + -2x2 Reorder the terms: 2x2 + -2x2 + -1y + -6y2 = -4x + xy + -2x2 Combine like terms: 2x2 + -2x2 = 0 0 + -1y + -6y2 = -4x + xy + -2x2 -1y + -6y2 = -4x + xy + -2x2 Add 'y' to each side of the equation. -1y + y + -6y2 = -4x + xy + -2x2 + y Combine like terms: -1y + y = 0 0 + -6y2 = -4x + xy + -2x2 + y -6y2 = -4x + xy + -2x2 + y Add '6y2' to each side of the equation. -6y2 + 6y2 = -4x + xy + -2x2 + y + 6y2 Combine like terms: -6y2 + 6y2 = 0 0 = -4x + xy + -2x2 + y + 6y2 Simplifying 0 = -4x + xy + -2x2 + y + 6y2 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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