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