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