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Simplifying (x5 + -6y + y3) * dx + (y4 + 6x + -1x3) * dy = 0 Reorder the terms for easier multiplication: dx(x5 + -6y + y3) + (y4 + 6x + -1x3) * dy = 0 (x5 * dx + -6y * dx + y3 * dx) + (y4 + 6x + -1x3) * dy = 0 Reorder the terms: (-6dxy + dxy3 + dx6) + (y4 + 6x + -1x3) * dy = 0 (-6dxy + dxy3 + dx6) + (y4 + 6x + -1x3) * dy = 0 Reorder the terms: -6dxy + dxy3 + dx6 + (6x + -1x3 + y4) * dy = 0 Reorder the terms for easier multiplication: -6dxy + dxy3 + dx6 + dy(6x + -1x3 + y4) = 0 -6dxy + dxy3 + dx6 + (6x * dy + -1x3 * dy + y4 * dy) = 0 -6dxy + dxy3 + dx6 + (6dxy + -1dx3y + dy5) = 0 Reorder the terms: -6dxy + 6dxy + dxy3 + -1dx3y + dx6 + dy5 = 0 Combine like terms: -6dxy + 6dxy = 0 0 + dxy3 + -1dx3y + dx6 + dy5 = 0 dxy3 + -1dx3y + dx6 + dy5 = 0 Solving dxy3 + -1dx3y + dx6 + dy5 = 0 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'd'. d(xy3 + -1x3y + x6 + y5) = 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 '(xy3 + -1x3y + x6 + y5)' equal to zero and attempt to solve: Simplifying xy3 + -1x3y + x6 + y5 = 0 Solving xy3 + -1x3y + x6 + y5 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1xy3' to each side of the equation. xy3 + -1x3y + x6 + -1xy3 + y5 = 0 + -1xy3 Reorder the terms: xy3 + -1xy3 + -1x3y + x6 + y5 = 0 + -1xy3 Combine like terms: xy3 + -1xy3 = 0 0 + -1x3y + x6 + y5 = 0 + -1xy3 -1x3y + x6 + y5 = 0 + -1xy3 Remove the zero: -1x3y + x6 + y5 = -1xy3 Add 'x3y' to each side of the equation. -1x3y + x6 + x3y + y5 = -1xy3 + x3y Reorder the terms: -1x3y + x3y + x6 + y5 = -1xy3 + x3y Combine like terms: -1x3y + x3y = 0 0 + x6 + y5 = -1xy3 + x3y x6 + y5 = -1xy3 + x3y Add '-1x6' to each side of the equation. x6 + -1x6 + y5 = -1xy3 + x3y + -1x6 Combine like terms: x6 + -1x6 = 0 0 + y5 = -1xy3 + x3y + -1x6 y5 = -1xy3 + x3y + -1x6 Add '-1y5' to each side of the equation. y5 + -1y5 = -1xy3 + x3y + -1x6 + -1y5 Combine like terms: y5 + -1y5 = 0 0 = -1xy3 + x3y + -1x6 + -1y5 Simplifying 0 = -1xy3 + x3y + -1x6 + -1y5 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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