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Simplifying (3x2 + 8xy + -2y2) * dx + (4x2 + -4y2 + -3g2) * dy = 0 Reorder the terms: (8xy + 3x2 + -2y2) * dx + (4x2 + -4y2 + -3g2) * dy = 0 Reorder the terms for easier multiplication: dx(8xy + 3x2 + -2y2) + (4x2 + -4y2 + -3g2) * dy = 0 (8xy * dx + 3x2 * dx + -2y2 * dx) + (4x2 + -4y2 + -3g2) * dy = 0 Reorder the terms: (-2dxy2 + 8dx2y + 3dx3) + (4x2 + -4y2 + -3g2) * dy = 0 (-2dxy2 + 8dx2y + 3dx3) + (4x2 + -4y2 + -3g2) * dy = 0 Reorder the terms: -2dxy2 + 8dx2y + 3dx3 + (-3g2 + 4x2 + -4y2) * dy = 0 Reorder the terms for easier multiplication: -2dxy2 + 8dx2y + 3dx3 + dy(-3g2 + 4x2 + -4y2) = 0 -2dxy2 + 8dx2y + 3dx3 + (-3g2 * dy + 4x2 * dy + -4y2 * dy) = 0 -2dxy2 + 8dx2y + 3dx3 + (-3dg2y + 4dx2y + -4dy3) = 0 Reorder the terms: -3dg2y + -2dxy2 + 8dx2y + 4dx2y + 3dx3 + -4dy3 = 0 Combine like terms: 8dx2y + 4dx2y = 12dx2y -3dg2y + -2dxy2 + 12dx2y + 3dx3 + -4dy3 = 0 Solving -3dg2y + -2dxy2 + 12dx2y + 3dx3 + -4dy3 = 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(-3g2y + -2xy2 + 12x2y + 3x3 + -4y3) = 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 '(-3g2y + -2xy2 + 12x2y + 3x3 + -4y3)' equal to zero and attempt to solve: Simplifying -3g2y + -2xy2 + 12x2y + 3x3 + -4y3 = 0 Solving -3g2y + -2xy2 + 12x2y + 3x3 + -4y3 = 0 Move all terms containing d to the left, all other terms to the right. Add '3g2y' to each side of the equation. -3g2y + -2xy2 + 12x2y + 3x3 + 3g2y + -4y3 = 0 + 3g2y Reorder the terms: -3g2y + 3g2y + -2xy2 + 12x2y + 3x3 + -4y3 = 0 + 3g2y Combine like terms: -3g2y + 3g2y = 0 0 + -2xy2 + 12x2y + 3x3 + -4y3 = 0 + 3g2y -2xy2 + 12x2y + 3x3 + -4y3 = 0 + 3g2y Remove the zero: -2xy2 + 12x2y + 3x3 + -4y3 = 3g2y Add '2xy2' to each side of the equation. -2xy2 + 12x2y + 3x3 + 2xy2 + -4y3 = 3g2y + 2xy2 Reorder the terms: -2xy2 + 2xy2 + 12x2y + 3x3 + -4y3 = 3g2y + 2xy2 Combine like terms: -2xy2 + 2xy2 = 0 0 + 12x2y + 3x3 + -4y3 = 3g2y + 2xy2 12x2y + 3x3 + -4y3 = 3g2y + 2xy2 Add '-12x2y' to each side of the equation. 12x2y + 3x3 + -12x2y + -4y3 = 3g2y + 2xy2 + -12x2y Reorder the terms: 12x2y + -12x2y + 3x3 + -4y3 = 3g2y + 2xy2 + -12x2y Combine like terms: 12x2y + -12x2y = 0 0 + 3x3 + -4y3 = 3g2y + 2xy2 + -12x2y 3x3 + -4y3 = 3g2y + 2xy2 + -12x2y Add '-3x3' to each side of the equation. 3x3 + -3x3 + -4y3 = 3g2y + 2xy2 + -12x2y + -3x3 Combine like terms: 3x3 + -3x3 = 0 0 + -4y3 = 3g2y + 2xy2 + -12x2y + -3x3 -4y3 = 3g2y + 2xy2 + -12x2y + -3x3 Add '4y3' to each side of the equation. -4y3 + 4y3 = 3g2y + 2xy2 + -12x2y + -3x3 + 4y3 Combine like terms: -4y3 + 4y3 = 0 0 = 3g2y + 2xy2 + -12x2y + -3x3 + 4y3 Simplifying 0 = 3g2y + 2xy2 + -12x2y + -3x3 + 4y3 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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