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