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Simplifying (4 + -3x + -3y) * dy = (y + x) * dx Reorder the terms for easier multiplication: dy(4 + -3x + -3y) = (y + x) * dx (4 * dy + -3x * dy + -3y * dy) = (y + x) * dx Reorder the terms: (-3dxy + 4dy + -3dy2) = (y + x) * dx (-3dxy + 4dy + -3dy2) = (y + x) * dx Reorder the terms: -3dxy + 4dy + -3dy2 = (x + y) * dx Reorder the terms for easier multiplication: -3dxy + 4dy + -3dy2 = dx(x + y) -3dxy + 4dy + -3dy2 = (x * dx + y * dx) Reorder the terms: -3dxy + 4dy + -3dy2 = (dxy + dx2) -3dxy + 4dy + -3dy2 = (dxy + dx2) Solving -3dxy + 4dy + -3dy2 = dxy + dx2 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. -3dxy + 4dy + -1dxy + -3dy2 = dxy + -1dxy + dx2 Reorder the terms: -3dxy + -1dxy + 4dy + -3dy2 = dxy + -1dxy + dx2 Combine like terms: -3dxy + -1dxy = -4dxy -4dxy + 4dy + -3dy2 = dxy + -1dxy + dx2 Combine like terms: dxy + -1dxy = 0 -4dxy + 4dy + -3dy2 = 0 + dx2 -4dxy + 4dy + -3dy2 = dx2 Add '-1dx2' to each side of the equation. -4dxy + 4dy + -1dx2 + -3dy2 = dx2 + -1dx2 Reorder the terms: -4dxy + -1dx2 + 4dy + -3dy2 = dx2 + -1dx2 Combine like terms: dx2 + -1dx2 = 0 -4dxy + -1dx2 + 4dy + -3dy2 = 0 Factor out the Greatest Common Factor (GCF), 'd'. d(-4xy + -1x2 + 4y + -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 '(-4xy + -1x2 + 4y + -3y2)' equal to zero and attempt to solve: Simplifying -4xy + -1x2 + 4y + -3y2 = 0 Solving -4xy + -1x2 + 4y + -3y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '4xy' to each side of the equation. -4xy + -1x2 + 4y + 4xy + -3y2 = 0 + 4xy Reorder the terms: -4xy + 4xy + -1x2 + 4y + -3y2 = 0 + 4xy Combine like terms: -4xy + 4xy = 0 0 + -1x2 + 4y + -3y2 = 0 + 4xy -1x2 + 4y + -3y2 = 0 + 4xy Remove the zero: -1x2 + 4y + -3y2 = 4xy Add 'x2' to each side of the equation. -1x2 + 4y + x2 + -3y2 = 4xy + x2 Reorder the terms: -1x2 + x2 + 4y + -3y2 = 4xy + x2 Combine like terms: -1x2 + x2 = 0 0 + 4y + -3y2 = 4xy + x2 4y + -3y2 = 4xy + x2 Add '-4y' to each side of the equation. 4y + -4y + -3y2 = 4xy + x2 + -4y Combine like terms: 4y + -4y = 0 0 + -3y2 = 4xy + x2 + -4y -3y2 = 4xy + x2 + -4y Add '3y2' to each side of the equation. -3y2 + 3y2 = 4xy + x2 + -4y + 3y2 Combine like terms: -3y2 + 3y2 = 0 0 = 4xy + x2 + -4y + 3y2 Simplifying 0 = 4xy + x2 + -4y + 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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