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Simplifying (x + 4)(y2 + 1) * dx + y(x2 + 3x + 2) * dy = 0 Reorder the terms: (4 + x)(y2 + 1) * dx + y(x2 + 3x + 2) * dy = 0 Reorder the terms: (4 + x)(1 + y2) * dx + y(x2 + 3x + 2) * dy = 0 Reorder the terms for easier multiplication: dx(4 + x)(1 + y2) + y(x2 + 3x + 2) * dy = 0 Multiply (4 + x) * (1 + y2) dx(4(1 + y2) + x(1 + y2)) + y(x2 + 3x + 2) * dy = 0 dx((1 * 4 + y2 * 4) + x(1 + y2)) + y(x2 + 3x + 2) * dy = 0 dx((4 + 4y2) + x(1 + y2)) + y(x2 + 3x + 2) * dy = 0 dx(4 + 4y2 + (1 * x + y2 * x)) + y(x2 + 3x + 2) * dy = 0 dx(4 + 4y2 + (1x + xy2)) + y(x2 + 3x + 2) * dy = 0 Reorder the terms: dx(4 + 1x + xy2 + 4y2) + y(x2 + 3x + 2) * dy = 0 dx(4 + 1x + xy2 + 4y2) + y(x2 + 3x + 2) * dy = 0 (4 * dx + 1x * dx + xy2 * dx + 4y2 * dx) + y(x2 + 3x + 2) * dy = 0 Reorder the terms: (4dx + 4dxy2 + 1dx2 + dx2y2) + y(x2 + 3x + 2) * dy = 0 (4dx + 4dxy2 + 1dx2 + dx2y2) + y(x2 + 3x + 2) * dy = 0 Reorder the terms: 4dx + 4dxy2 + 1dx2 + dx2y2 + y(2 + 3x + x2) * dy = 0 Reorder the terms for easier multiplication: 4dx + 4dxy2 + 1dx2 + dx2y2 + y * dy(2 + 3x + x2) = 0 Multiply y * dy 4dx + 4dxy2 + 1dx2 + dx2y2 + dy2(2 + 3x + x2) = 0 4dx + 4dxy2 + 1dx2 + dx2y2 + (2 * dy2 + 3x * dy2 + x2 * dy2) = 0 Reorder the terms: 4dx + 4dxy2 + 1dx2 + dx2y2 + (3dxy2 + dx2y2 + 2dy2) = 0 4dx + 4dxy2 + 1dx2 + dx2y2 + (3dxy2 + dx2y2 + 2dy2) = 0 Reorder the terms: 4dx + 4dxy2 + 3dxy2 + 1dx2 + dx2y2 + dx2y2 + 2dy2 = 0 Combine like terms: 4dxy2 + 3dxy2 = 7dxy2 4dx + 7dxy2 + 1dx2 + dx2y2 + dx2y2 + 2dy2 = 0 Combine like terms: dx2y2 + dx2y2 = 2dx2y2 4dx + 7dxy2 + 1dx2 + 2dx2y2 + 2dy2 = 0 Solving 4dx + 7dxy2 + 1dx2 + 2dx2y2 + 2dy2 = 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(4x + 7xy2 + x2 + 2x2y2 + 2y2) = 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 + 7xy2 + x2 + 2x2y2 + 2y2)' equal to zero and attempt to solve: Simplifying 4x + 7xy2 + x2 + 2x2y2 + 2y2 = 0 Solving 4x + 7xy2 + x2 + 2x2y2 + 2y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-4x' to each side of the equation. 4x + 7xy2 + x2 + 2x2y2 + -4x + 2y2 = 0 + -4x Reorder the terms: 4x + -4x + 7xy2 + x2 + 2x2y2 + 2y2 = 0 + -4x Combine like terms: 4x + -4x = 0 0 + 7xy2 + x2 + 2x2y2 + 2y2 = 0 + -4x 7xy2 + x2 + 2x2y2 + 2y2 = 0 + -4x Remove the zero: 7xy2 + x2 + 2x2y2 + 2y2 = -4x Add '-7xy2' to each side of the equation. 7xy2 + x2 + 2x2y2 + -7xy2 + 2y2 = -4x + -7xy2 Reorder the terms: 7xy2 + -7xy2 + x2 + 2x2y2 + 2y2 = -4x + -7xy2 Combine like terms: 7xy2 + -7xy2 = 0 0 + x2 + 2x2y2 + 2y2 = -4x + -7xy2 x2 + 2x2y2 + 2y2 = -4x + -7xy2 Add '-1x2' to each side of the equation. x2 + 2x2y2 + -1x2 + 2y2 = -4x + -7xy2 + -1x2 Reorder the terms: x2 + -1x2 + 2x2y2 + 2y2 = -4x + -7xy2 + -1x2 Combine like terms: x2 + -1x2 = 0 0 + 2x2y2 + 2y2 = -4x + -7xy2 + -1x2 2x2y2 + 2y2 = -4x + -7xy2 + -1x2 Add '-2x2y2' to each side of the equation. 2x2y2 + -2x2y2 + 2y2 = -4x + -7xy2 + -1x2 + -2x2y2 Combine like terms: 2x2y2 + -2x2y2 = 0 0 + 2y2 = -4x + -7xy2 + -1x2 + -2x2y2 2y2 = -4x + -7xy2 + -1x2 + -2x2y2 Add '-2y2' to each side of the equation. 2y2 + -2y2 = -4x + -7xy2 + -1x2 + -2x2y2 + -2y2 Combine like terms: 2y2 + -2y2 = 0 0 = -4x + -7xy2 + -1x2 + -2x2y2 + -2y2 Simplifying 0 = -4x + -7xy2 + -1x2 + -2x2y2 + -2y2 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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