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