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Simplifying (3x + 8)(y2 + 4) * dx + -4y(x2 + 5x + 6) * dy = 0 Reorder the terms: (8 + 3x)(y2 + 4) * dx + -4y(x2 + 5x + 6) * dy = 0 Reorder the terms: (8 + 3x)(4 + y2) * dx + -4y(x2 + 5x + 6) * dy = 0 Reorder the terms for easier multiplication: dx(8 + 3x)(4 + y2) + -4y(x2 + 5x + 6) * dy = 0 Multiply (8 + 3x) * (4 + y2) dx(8(4 + y2) + 3x * (4 + y2)) + -4y(x2 + 5x + 6) * dy = 0 dx((4 * 8 + y2 * 8) + 3x * (4 + y2)) + -4y(x2 + 5x + 6) * dy = 0 dx((32 + 8y2) + 3x * (4 + y2)) + -4y(x2 + 5x + 6) * dy = 0 dx(32 + 8y2 + (4 * 3x + y2 * 3x)) + -4y(x2 + 5x + 6) * dy = 0 dx(32 + 8y2 + (12x + 3xy2)) + -4y(x2 + 5x + 6) * dy = 0 Reorder the terms: dx(32 + 12x + 3xy2 + 8y2) + -4y(x2 + 5x + 6) * dy = 0 dx(32 + 12x + 3xy2 + 8y2) + -4y(x2 + 5x + 6) * dy = 0 (32 * dx + 12x * dx + 3xy2 * dx + 8y2 * dx) + -4y(x2 + 5x + 6) * dy = 0 Reorder the terms: (32dx + 8dxy2 + 12dx2 + 3dx2y2) + -4y(x2 + 5x + 6) * dy = 0 (32dx + 8dxy2 + 12dx2 + 3dx2y2) + -4y(x2 + 5x + 6) * dy = 0 Reorder the terms: 32dx + 8dxy2 + 12dx2 + 3dx2y2 + -4y(6 + 5x + x2) * dy = 0 Reorder the terms for easier multiplication: 32dx + 8dxy2 + 12dx2 + 3dx2y2 + -4y * dy(6 + 5x + x2) = 0 Multiply y * dy 32dx + 8dxy2 + 12dx2 + 3dx2y2 + -4dy2(6 + 5x + x2) = 0 32dx + 8dxy2 + 12dx2 + 3dx2y2 + (6 * -4dy2 + 5x * -4dy2 + x2 * -4dy2) = 0 Reorder the terms: 32dx + 8dxy2 + 12dx2 + 3dx2y2 + (-20dxy2 + -4dx2y2 + -24dy2) = 0 32dx + 8dxy2 + 12dx2 + 3dx2y2 + (-20dxy2 + -4dx2y2 + -24dy2) = 0 Reorder the terms: 32dx + 8dxy2 + -20dxy2 + 12dx2 + 3dx2y2 + -4dx2y2 + -24dy2 = 0 Combine like terms: 8dxy2 + -20dxy2 = -12dxy2 32dx + -12dxy2 + 12dx2 + 3dx2y2 + -4dx2y2 + -24dy2 = 0 Combine like terms: 3dx2y2 + -4dx2y2 = -1dx2y2 32dx + -12dxy2 + 12dx2 + -1dx2y2 + -24dy2 = 0 Solving 32dx + -12dxy2 + 12dx2 + -1dx2y2 + -24dy2 = 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(32x + -12xy2 + 12x2 + -1x2y2 + -24y2) = 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 '(32x + -12xy2 + 12x2 + -1x2y2 + -24y2)' equal to zero and attempt to solve: Simplifying 32x + -12xy2 + 12x2 + -1x2y2 + -24y2 = 0 Solving 32x + -12xy2 + 12x2 + -1x2y2 + -24y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-32x' to each side of the equation. 32x + -12xy2 + 12x2 + -1x2y2 + -32x + -24y2 = 0 + -32x Reorder the terms: 32x + -32x + -12xy2 + 12x2 + -1x2y2 + -24y2 = 0 + -32x Combine like terms: 32x + -32x = 0 0 + -12xy2 + 12x2 + -1x2y2 + -24y2 = 0 + -32x -12xy2 + 12x2 + -1x2y2 + -24y2 = 0 + -32x Remove the zero: -12xy2 + 12x2 + -1x2y2 + -24y2 = -32x Add '12xy2' to each side of the equation. -12xy2 + 12x2 + -1x2y2 + 12xy2 + -24y2 = -32x + 12xy2 Reorder the terms: -12xy2 + 12xy2 + 12x2 + -1x2y2 + -24y2 = -32x + 12xy2 Combine like terms: -12xy2 + 12xy2 = 0 0 + 12x2 + -1x2y2 + -24y2 = -32x + 12xy2 12x2 + -1x2y2 + -24y2 = -32x + 12xy2 Add '-12x2' to each side of the equation. 12x2 + -1x2y2 + -12x2 + -24y2 = -32x + 12xy2 + -12x2 Reorder the terms: 12x2 + -12x2 + -1x2y2 + -24y2 = -32x + 12xy2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 0 + -1x2y2 + -24y2 = -32x + 12xy2 + -12x2 -1x2y2 + -24y2 = -32x + 12xy2 + -12x2 Add 'x2y2' to each side of the equation. -1x2y2 + x2y2 + -24y2 = -32x + 12xy2 + -12x2 + x2y2 Combine like terms: -1x2y2 + x2y2 = 0 0 + -24y2 = -32x + 12xy2 + -12x2 + x2y2 -24y2 = -32x + 12xy2 + -12x2 + x2y2 Add '24y2' to each side of the equation. -24y2 + 24y2 = -32x + 12xy2 + -12x2 + x2y2 + 24y2 Combine like terms: -24y2 + 24y2 = 0 0 = -32x + 12xy2 + -12x2 + x2y2 + 24y2 Simplifying 0 = -32x + 12xy2 + -12x2 + x2y2 + 24y2 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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