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Simplifying (6xy + 5y4) * dx + (4x2 + 7xy3) * dy = 0 Reorder the terms for easier multiplication: dx(6xy + 5y4) + (4x2 + 7xy3) * dy = 0 (6xy * dx + 5y4 * dx) + (4x2 + 7xy3) * dy = 0 Reorder the terms: (5dxy4 + 6dx2y) + (4x2 + 7xy3) * dy = 0 (5dxy4 + 6dx2y) + (4x2 + 7xy3) * dy = 0 Reorder the terms: 5dxy4 + 6dx2y + (7xy3 + 4x2) * dy = 0 Reorder the terms for easier multiplication: 5dxy4 + 6dx2y + dy(7xy3 + 4x2) = 0 5dxy4 + 6dx2y + (7xy3 * dy + 4x2 * dy) = 0 5dxy4 + 6dx2y + (7dxy4 + 4dx2y) = 0 Reorder the terms: 5dxy4 + 7dxy4 + 6dx2y + 4dx2y = 0 Combine like terms: 5dxy4 + 7dxy4 = 12dxy4 12dxy4 + 6dx2y + 4dx2y = 0 Combine like terms: 6dx2y + 4dx2y = 10dx2y 12dxy4 + 10dx2y = 0 Solving 12dxy4 + 10dx2y = 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), '2dxy'. 2dxy(6y3 + 5x) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'dxy' equal to zero and attempt to solve: Simplifying dxy = 0 Solving dxy = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dxy = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(6y3 + 5x)' equal to zero and attempt to solve: Simplifying 6y3 + 5x = 0 Reorder the terms: 5x + 6y3 = 0 Solving 5x + 6y3 = 0 Move all terms containing d to the left, all other terms to the right. Add '-5x' to each side of the equation. 5x + -5x + 6y3 = 0 + -5x Combine like terms: 5x + -5x = 0 0 + 6y3 = 0 + -5x 6y3 = 0 + -5x Remove the zero: 6y3 = -5x Add '-6y3' to each side of the equation. 6y3 + -6y3 = -5x + -6y3 Combine like terms: 6y3 + -6y3 = 0 0 = -5x + -6y3 Simplifying 0 = -5x + -6y3 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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