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