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