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Simplifying (2x + 3y + 4) * dy + -1(4x + 6y + 5) * dx = 0 Reorder the terms: (4 + 2x + 3y) * dy + -1(4x + 6y + 5) * dx = 0 Reorder the terms for easier multiplication: dy(4 + 2x + 3y) + -1(4x + 6y + 5) * dx = 0 (4 * dy + 2x * dy + 3y * dy) + -1(4x + 6y + 5) * dx = 0 Reorder the terms: (2dxy + 4dy + 3dy2) + -1(4x + 6y + 5) * dx = 0 (2dxy + 4dy + 3dy2) + -1(4x + 6y + 5) * dx = 0 Reorder the terms: 2dxy + 4dy + 3dy2 + -1(5 + 4x + 6y) * dx = 0 Reorder the terms for easier multiplication: 2dxy + 4dy + 3dy2 + -1dx(5 + 4x + 6y) = 0 2dxy + 4dy + 3dy2 + (5 * -1dx + 4x * -1dx + 6y * -1dx) = 0 Reorder the terms: 2dxy + 4dy + 3dy2 + (-5dx + -6dxy + -4dx2) = 0 2dxy + 4dy + 3dy2 + (-5dx + -6dxy + -4dx2) = 0 Reorder the terms: -5dx + 2dxy + -6dxy + -4dx2 + 4dy + 3dy2 = 0 Combine like terms: 2dxy + -6dxy = -4dxy -5dx + -4dxy + -4dx2 + 4dy + 3dy2 = 0 Solving -5dx + -4dxy + -4dx2 + 4dy + 3dy2 = 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), 'd'. d(-5x + -4xy + -4x2 + 4y + 3y2) = 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 '(-5x + -4xy + -4x2 + 4y + 3y2)' equal to zero and attempt to solve: Simplifying -5x + -4xy + -4x2 + 4y + 3y2 = 0 Solving -5x + -4xy + -4x2 + 4y + 3y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '5x' to each side of the equation. -5x + -4xy + -4x2 + 4y + 5x + 3y2 = 0 + 5x Reorder the terms: -5x + 5x + -4xy + -4x2 + 4y + 3y2 = 0 + 5x Combine like terms: -5x + 5x = 0 0 + -4xy + -4x2 + 4y + 3y2 = 0 + 5x -4xy + -4x2 + 4y + 3y2 = 0 + 5x Remove the zero: -4xy + -4x2 + 4y + 3y2 = 5x Add '4xy' to each side of the equation. -4xy + -4x2 + 4y + 4xy + 3y2 = 5x + 4xy Reorder the terms: -4xy + 4xy + -4x2 + 4y + 3y2 = 5x + 4xy Combine like terms: -4xy + 4xy = 0 0 + -4x2 + 4y + 3y2 = 5x + 4xy -4x2 + 4y + 3y2 = 5x + 4xy Add '4x2' to each side of the equation. -4x2 + 4y + 4x2 + 3y2 = 5x + 4xy + 4x2 Reorder the terms: -4x2 + 4x2 + 4y + 3y2 = 5x + 4xy + 4x2 Combine like terms: -4x2 + 4x2 = 0 0 + 4y + 3y2 = 5x + 4xy + 4x2 4y + 3y2 = 5x + 4xy + 4x2 Add '-4y' to each side of the equation. 4y + -4y + 3y2 = 5x + 4xy + 4x2 + -4y Combine like terms: 4y + -4y = 0 0 + 3y2 = 5x + 4xy + 4x2 + -4y 3y2 = 5x + 4xy + 4x2 + -4y Add '-3y2' to each side of the equation. 3y2 + -3y2 = 5x + 4xy + 4x2 + -4y + -3y2 Combine like terms: 3y2 + -3y2 = 0 0 = 5x + 4xy + 4x2 + -4y + -3y2 Simplifying 0 = 5x + 4xy + 4x2 + -4y + -3y2 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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