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Simplifying (2x + 3y + -1) * dx = (6x + 9y + 6) * dy Reorder the terms: (-1 + 2x + 3y) * dx = (6x + 9y + 6) * dy Reorder the terms for easier multiplication: dx(-1 + 2x + 3y) = (6x + 9y + 6) * dy (-1 * dx + 2x * dx + 3y * dx) = (6x + 9y + 6) * dy Reorder the terms: (-1dx + 3dxy + 2dx2) = (6x + 9y + 6) * dy (-1dx + 3dxy + 2dx2) = (6x + 9y + 6) * dy Reorder the terms: -1dx + 3dxy + 2dx2 = (6 + 6x + 9y) * dy Reorder the terms for easier multiplication: -1dx + 3dxy + 2dx2 = dy(6 + 6x + 9y) -1dx + 3dxy + 2dx2 = (6 * dy + 6x * dy + 9y * dy) Reorder the terms: -1dx + 3dxy + 2dx2 = (6dxy + 6dy + 9dy2) -1dx + 3dxy + 2dx2 = (6dxy + 6dy + 9dy2) Solving -1dx + 3dxy + 2dx2 = 6dxy + 6dy + 9dy2 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-6dxy' to each side of the equation. -1dx + 3dxy + -6dxy + 2dx2 = 6dxy + 6dy + -6dxy + 9dy2 Combine like terms: 3dxy + -6dxy = -3dxy -1dx + -3dxy + 2dx2 = 6dxy + 6dy + -6dxy + 9dy2 Reorder the terms: -1dx + -3dxy + 2dx2 = 6dxy + -6dxy + 6dy + 9dy2 Combine like terms: 6dxy + -6dxy = 0 -1dx + -3dxy + 2dx2 = 0 + 6dy + 9dy2 -1dx + -3dxy + 2dx2 = 6dy + 9dy2 Add '-6dy' to each side of the equation. -1dx + -3dxy + 2dx2 + -6dy = 6dy + -6dy + 9dy2 Combine like terms: 6dy + -6dy = 0 -1dx + -3dxy + 2dx2 + -6dy = 0 + 9dy2 -1dx + -3dxy + 2dx2 + -6dy = 9dy2 Add '-9dy2' to each side of the equation. -1dx + -3dxy + 2dx2 + -6dy + -9dy2 = 9dy2 + -9dy2 Combine like terms: 9dy2 + -9dy2 = 0 -1dx + -3dxy + 2dx2 + -6dy + -9dy2 = 0 Factor out the Greatest Common Factor (GCF), 'd'. d(-1x + -3xy + 2x2 + -6y + -9y2) = 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 + -3xy + 2x2 + -6y + -9y2)' equal to zero and attempt to solve: Simplifying -1x + -3xy + 2x2 + -6y + -9y2 = 0 Solving -1x + -3xy + 2x2 + -6y + -9y2 = 0 Move all terms containing d to the left, all other terms to the right. Add 'x' to each side of the equation. -1x + -3xy + 2x2 + -6y + x + -9y2 = 0 + x Reorder the terms: -1x + x + -3xy + 2x2 + -6y + -9y2 = 0 + x Combine like terms: -1x + x = 0 0 + -3xy + 2x2 + -6y + -9y2 = 0 + x -3xy + 2x2 + -6y + -9y2 = 0 + x Remove the zero: -3xy + 2x2 + -6y + -9y2 = x Add '3xy' to each side of the equation. -3xy + 2x2 + -6y + 3xy + -9y2 = x + 3xy Reorder the terms: -3xy + 3xy + 2x2 + -6y + -9y2 = x + 3xy Combine like terms: -3xy + 3xy = 0 0 + 2x2 + -6y + -9y2 = x + 3xy 2x2 + -6y + -9y2 = x + 3xy Add '-2x2' to each side of the equation. 2x2 + -6y + -2x2 + -9y2 = x + 3xy + -2x2 Reorder the terms: 2x2 + -2x2 + -6y + -9y2 = x + 3xy + -2x2 Combine like terms: 2x2 + -2x2 = 0 0 + -6y + -9y2 = x + 3xy + -2x2 -6y + -9y2 = x + 3xy + -2x2 Add '6y' to each side of the equation. -6y + 6y + -9y2 = x + 3xy + -2x2 + 6y Combine like terms: -6y + 6y = 0 0 + -9y2 = x + 3xy + -2x2 + 6y -9y2 = x + 3xy + -2x2 + 6y Add '9y2' to each side of the equation. -9y2 + 9y2 = x + 3xy + -2x2 + 6y + 9y2 Combine like terms: -9y2 + 9y2 = 0 0 = x + 3xy + -2x2 + 6y + 9y2 Simplifying 0 = x + 3xy + -2x2 + 6y + 9y2 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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