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