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Simplifying y(12 + 5xy) * dx + x(6 + 3xy) * dy = 0 Reorder the terms for easier multiplication: y * dx(12 + 5xy) + x(6 + 3xy) * dy = 0 Multiply y * dx dxy(12 + 5xy) + x(6 + 3xy) * dy = 0 (12 * dxy + 5xy * dxy) + x(6 + 3xy) * dy = 0 (12dxy + 5dx2y2) + x(6 + 3xy) * dy = 0 Reorder the terms for easier multiplication: 12dxy + 5dx2y2 + x * dy(6 + 3xy) = 0 Multiply x * dy 12dxy + 5dx2y2 + dxy(6 + 3xy) = 0 12dxy + 5dx2y2 + (6 * dxy + 3xy * dxy) = 0 12dxy + 5dx2y2 + (6dxy + 3dx2y2) = 0 Reorder the terms: 12dxy + 6dxy + 5dx2y2 + 3dx2y2 = 0 Combine like terms: 12dxy + 6dxy = 18dxy 18dxy + 5dx2y2 + 3dx2y2 = 0 Combine like terms: 5dx2y2 + 3dx2y2 = 8dx2y2 18dxy + 8dx2y2 = 0 Solving 18dxy + 8dx2y2 = 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(9 + 4xy) = 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 '(9 + 4xy)' equal to zero and attempt to solve: Simplifying 9 + 4xy = 0 Solving 9 + 4xy = 0 Move all terms containing d to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 4xy = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 4xy = 0 + -9 4xy = 0 + -9 Combine like terms: 0 + -9 = -9 4xy = -9 Add '-4xy' to each side of the equation. 4xy + -4xy = -9 + -4xy Combine like terms: 4xy + -4xy = 0 0 = -9 + -4xy Simplifying 0 = -9 + -4xy 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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