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