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