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Simplifying dy(x + y + -6) = dx(x + y + 4) Reorder the terms: dy(-6 + x + y) = dx(x + y + 4) (-6 * dy + x * dy + y * dy) = dx(x + y + 4) Reorder the terms: (dxy + -6dy + dy2) = dx(x + y + 4) (dxy + -6dy + dy2) = dx(x + y + 4) Reorder the terms: dxy + -6dy + dy2 = dx(4 + x + y) dxy + -6dy + dy2 = (4 * dx + x * dx + y * dx) Reorder the terms: dxy + -6dy + dy2 = (4dx + dxy + dx2) dxy + -6dy + dy2 = (4dx + dxy + dx2) Add '-1dxy' to each side of the equation. dxy + -6dy + -1dxy + dy2 = 4dx + dxy + -1dxy + dx2 Reorder the terms: dxy + -1dxy + -6dy + dy2 = 4dx + dxy + -1dxy + dx2 Combine like terms: dxy + -1dxy = 0 0 + -6dy + dy2 = 4dx + dxy + -1dxy + dx2 -6dy + dy2 = 4dx + dxy + -1dxy + dx2 Combine like terms: dxy + -1dxy = 0 -6dy + dy2 = 4dx + 0 + dx2 -6dy + dy2 = 4dx + dx2 Solving -6dy + dy2 = 4dx + dx2 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-4dx' to each side of the equation. -6dy + -4dx + dy2 = 4dx + -4dx + dx2 Reorder the terms: -4dx + -6dy + dy2 = 4dx + -4dx + dx2 Combine like terms: 4dx + -4dx = 0 -4dx + -6dy + dy2 = 0 + dx2 -4dx + -6dy + dy2 = dx2 Add '-1dx2' to each side of the equation. -4dx + -6dy + -1dx2 + dy2 = dx2 + -1dx2 Reorder the terms: -4dx + -1dx2 + -6dy + dy2 = dx2 + -1dx2 Combine like terms: dx2 + -1dx2 = 0 -4dx + -1dx2 + -6dy + dy2 = 0 Factor out the Greatest Common Factor (GCF), 'd'. d(-4x + -1x2 + -6y + y2) = 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 '(-4x + -1x2 + -6y + y2)' equal to zero and attempt to solve: Simplifying -4x + -1x2 + -6y + y2 = 0 Solving -4x + -1x2 + -6y + y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '4x' to each side of the equation. -4x + -1x2 + -6y + 4x + y2 = 0 + 4x Reorder the terms: -4x + 4x + -1x2 + -6y + y2 = 0 + 4x Combine like terms: -4x + 4x = 0 0 + -1x2 + -6y + y2 = 0 + 4x -1x2 + -6y + y2 = 0 + 4x Remove the zero: -1x2 + -6y + y2 = 4x Add 'x2' to each side of the equation. -1x2 + -6y + x2 + y2 = 4x + x2 Reorder the terms: -1x2 + x2 + -6y + y2 = 4x + x2 Combine like terms: -1x2 + x2 = 0 0 + -6y + y2 = 4x + x2 -6y + y2 = 4x + x2 Add '6y' to each side of the equation. -6y + 6y + y2 = 4x + x2 + 6y Combine like terms: -6y + 6y = 0 0 + y2 = 4x + x2 + 6y y2 = 4x + x2 + 6y Add '-1y2' to each side of the equation. y2 + -1y2 = 4x + x2 + 6y + -1y2 Combine like terms: y2 + -1y2 = 0 0 = 4x + x2 + 6y + -1y2 Simplifying 0 = 4x + x2 + 6y + -1y2 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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