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Simplifying 2x(1 + y2) * dxy(1 + 2x2) * dy = 0 Reorder the terms for easier multiplication: 2x * dxy * dy(1 + y2)(1 + 2x2) = 0 Multiply x * dxy 2dx2y * dy(1 + y2)(1 + 2x2) = 0 Multiply dx2y * dy 2d2x2y2(1 + y2)(1 + 2x2) = 0 Multiply (1 + y2) * (1 + 2x2) 2d2x2y2(1(1 + 2x2) + y2(1 + 2x2)) = 0 2d2x2y2((1 * 1 + 2x2 * 1) + y2(1 + 2x2)) = 0 2d2x2y2((1 + 2x2) + y2(1 + 2x2)) = 0 2d2x2y2(1 + 2x2 + (1 * y2 + 2x2 * y2)) = 0 Reorder the terms: 2d2x2y2(1 + 2x2 + (2x2y2 + 1y2)) = 0 2d2x2y2(1 + 2x2 + (2x2y2 + 1y2)) = 0 2d2x2y2(1 + 2x2 + 2x2y2 + 1y2) = 0 (1 * 2d2x2y2 + 2x2 * 2d2x2y2 + 2x2y2 * 2d2x2y2 + 1y2 * 2d2x2y2) = 0 Reorder the terms: (2d2x2y2 + 2d2x2y4 + 4d2x4y2 + 4d2x4y4) = 0 (2d2x2y2 + 2d2x2y4 + 4d2x4y2 + 4d2x4y4) = 0 Solving 2d2x2y2 + 2d2x2y4 + 4d2x4y2 + 4d2x4y4 = 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), '2d2x2y2'. 2d2x2y2(1 + y2 + 2x2 + 2x2y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'd2x2y2' equal to zero and attempt to solve: Simplifying d2x2y2 = 0 Solving d2x2y2 = 0 Move all terms containing d to the left, all other terms to the right. Simplifying d2x2y2 = 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 '(1 + y2 + 2x2 + 2x2y2)' equal to zero and attempt to solve: Simplifying 1 + y2 + 2x2 + 2x2y2 = 0 Reorder the terms: 1 + 2x2 + 2x2y2 + y2 = 0 Solving 1 + 2x2 + 2x2y2 + y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + 2x2 + 2x2y2 + -1 + y2 = 0 + -1 Reorder the terms: 1 + -1 + 2x2 + 2x2y2 + y2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x2 + 2x2y2 + y2 = 0 + -1 2x2 + 2x2y2 + y2 = 0 + -1 Combine like terms: 0 + -1 = -1 2x2 + 2x2y2 + y2 = -1 Add '-2x2' to each side of the equation. 2x2 + 2x2y2 + -2x2 + y2 = -1 + -2x2 Reorder the terms: 2x2 + -2x2 + 2x2y2 + y2 = -1 + -2x2 Combine like terms: 2x2 + -2x2 = 0 0 + 2x2y2 + y2 = -1 + -2x2 2x2y2 + y2 = -1 + -2x2 Add '-2x2y2' to each side of the equation. 2x2y2 + -2x2y2 + y2 = -1 + -2x2 + -2x2y2 Combine like terms: 2x2y2 + -2x2y2 = 0 0 + y2 = -1 + -2x2 + -2x2y2 y2 = -1 + -2x2 + -2x2y2 Add '-1y2' to each side of the equation. y2 + -1y2 = -1 + -2x2 + -2x2y2 + -1y2 Combine like terms: y2 + -1y2 = 0 0 = -1 + -2x2 + -2x2y2 + -1y2 Simplifying 0 = -1 + -2x2 + -2x2y2 + -1y2 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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