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