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Simplifying (2x + -5y + 3) * dx + -1(2x + 4y + -6) * dy = 0 Reorder the terms: (3 + 2x + -5y) * dx + -1(2x + 4y + -6) * dy = 0 Reorder the terms for easier multiplication: dx(3 + 2x + -5y) + -1(2x + 4y + -6) * dy = 0 (3 * dx + 2x * dx + -5y * dx) + -1(2x + 4y + -6) * dy = 0 Reorder the terms: (3dx + -5dxy + 2dx2) + -1(2x + 4y + -6) * dy = 0 (3dx + -5dxy + 2dx2) + -1(2x + 4y + -6) * dy = 0 Reorder the terms: 3dx + -5dxy + 2dx2 + -1(-6 + 2x + 4y) * dy = 0 Reorder the terms for easier multiplication: 3dx + -5dxy + 2dx2 + -1dy(-6 + 2x + 4y) = 0 3dx + -5dxy + 2dx2 + (-6 * -1dy + 2x * -1dy + 4y * -1dy) = 0 Reorder the terms: 3dx + -5dxy + 2dx2 + (-2dxy + 6dy + -4dy2) = 0 3dx + -5dxy + 2dx2 + (-2dxy + 6dy + -4dy2) = 0 Reorder the terms: 3dx + -5dxy + -2dxy + 2dx2 + 6dy + -4dy2 = 0 Combine like terms: -5dxy + -2dxy = -7dxy 3dx + -7dxy + 2dx2 + 6dy + -4dy2 = 0 Solving 3dx + -7dxy + 2dx2 + 6dy + -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(3x + -7xy + 2x2 + 6y + -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 '(3x + -7xy + 2x2 + 6y + -4y2)' equal to zero and attempt to solve: Simplifying 3x + -7xy + 2x2 + 6y + -4y2 = 0 Solving 3x + -7xy + 2x2 + 6y + -4y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-3x' to each side of the equation. 3x + -7xy + 2x2 + 6y + -3x + -4y2 = 0 + -3x Reorder the terms: 3x + -3x + -7xy + 2x2 + 6y + -4y2 = 0 + -3x Combine like terms: 3x + -3x = 0 0 + -7xy + 2x2 + 6y + -4y2 = 0 + -3x -7xy + 2x2 + 6y + -4y2 = 0 + -3x Remove the zero: -7xy + 2x2 + 6y + -4y2 = -3x Add '7xy' to each side of the equation. -7xy + 2x2 + 6y + 7xy + -4y2 = -3x + 7xy Reorder the terms: -7xy + 7xy + 2x2 + 6y + -4y2 = -3x + 7xy Combine like terms: -7xy + 7xy = 0 0 + 2x2 + 6y + -4y2 = -3x + 7xy 2x2 + 6y + -4y2 = -3x + 7xy Add '-2x2' to each side of the equation. 2x2 + 6y + -2x2 + -4y2 = -3x + 7xy + -2x2 Reorder the terms: 2x2 + -2x2 + 6y + -4y2 = -3x + 7xy + -2x2 Combine like terms: 2x2 + -2x2 = 0 0 + 6y + -4y2 = -3x + 7xy + -2x2 6y + -4y2 = -3x + 7xy + -2x2 Add '-6y' to each side of the equation. 6y + -6y + -4y2 = -3x + 7xy + -2x2 + -6y Combine like terms: 6y + -6y = 0 0 + -4y2 = -3x + 7xy + -2x2 + -6y -4y2 = -3x + 7xy + -2x2 + -6y Add '4y2' to each side of the equation. -4y2 + 4y2 = -3x + 7xy + -2x2 + -6y + 4y2 Combine like terms: -4y2 + 4y2 = 0 0 = -3x + 7xy + -2x2 + -6y + 4y2 Simplifying 0 = -3x + 7xy + -2x2 + -6y + 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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