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Simplifying (4x2 + 3xy + y2) * dx = (4y2 + 3xy + x2) * dy Reorder the terms: (3xy + 4x2 + y2) * dx = (4y2 + 3xy + x2) * dy Reorder the terms for easier multiplication: dx(3xy + 4x2 + y2) = (4y2 + 3xy + x2) * dy (3xy * dx + 4x2 * dx + y2 * dx) = (4y2 + 3xy + x2) * dy Reorder the terms: (dxy2 + 3dx2y + 4dx3) = (4y2 + 3xy + x2) * dy (dxy2 + 3dx2y + 4dx3) = (4y2 + 3xy + x2) * dy Reorder the terms: dxy2 + 3dx2y + 4dx3 = (3xy + x2 + 4y2) * dy Reorder the terms for easier multiplication: dxy2 + 3dx2y + 4dx3 = dy(3xy + x2 + 4y2) dxy2 + 3dx2y + 4dx3 = (3xy * dy + x2 * dy + 4y2 * dy) dxy2 + 3dx2y + 4dx3 = (3dxy2 + dx2y + 4dy3) Solving dxy2 + 3dx2y + 4dx3 = 3dxy2 + dx2y + 4dy3 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-3dxy2' to each side of the equation. dxy2 + 3dx2y + -3dxy2 + 4dx3 = 3dxy2 + dx2y + -3dxy2 + 4dy3 Reorder the terms: dxy2 + -3dxy2 + 3dx2y + 4dx3 = 3dxy2 + dx2y + -3dxy2 + 4dy3 Combine like terms: dxy2 + -3dxy2 = -2dxy2 -2dxy2 + 3dx2y + 4dx3 = 3dxy2 + dx2y + -3dxy2 + 4dy3 Reorder the terms: -2dxy2 + 3dx2y + 4dx3 = 3dxy2 + -3dxy2 + dx2y + 4dy3 Combine like terms: 3dxy2 + -3dxy2 = 0 -2dxy2 + 3dx2y + 4dx3 = 0 + dx2y + 4dy3 -2dxy2 + 3dx2y + 4dx3 = dx2y + 4dy3 Add '-1dx2y' to each side of the equation. -2dxy2 + 3dx2y + -1dx2y + 4dx3 = dx2y + -1dx2y + 4dy3 Combine like terms: 3dx2y + -1dx2y = 2dx2y -2dxy2 + 2dx2y + 4dx3 = dx2y + -1dx2y + 4dy3 Combine like terms: dx2y + -1dx2y = 0 -2dxy2 + 2dx2y + 4dx3 = 0 + 4dy3 -2dxy2 + 2dx2y + 4dx3 = 4dy3 Add '-4dy3' to each side of the equation. -2dxy2 + 2dx2y + 4dx3 + -4dy3 = 4dy3 + -4dy3 Combine like terms: 4dy3 + -4dy3 = 0 -2dxy2 + 2dx2y + 4dx3 + -4dy3 = 0 Factor out the Greatest Common Factor (GCF), '2d'. 2d(-1xy2 + x2y + 2x3 + -2y3) = 0 Ignore the factor 2.Subproblem 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 '(-1xy2 + x2y + 2x3 + -2y3)' equal to zero and attempt to solve: Simplifying -1xy2 + x2y + 2x3 + -2y3 = 0 Solving -1xy2 + x2y + 2x3 + -2y3 = 0 Move all terms containing d to the left, all other terms to the right. Add 'xy2' to each side of the equation. -1xy2 + x2y + 2x3 + xy2 + -2y3 = 0 + xy2 Reorder the terms: -1xy2 + xy2 + x2y + 2x3 + -2y3 = 0 + xy2 Combine like terms: -1xy2 + xy2 = 0 0 + x2y + 2x3 + -2y3 = 0 + xy2 x2y + 2x3 + -2y3 = 0 + xy2 Remove the zero: x2y + 2x3 + -2y3 = xy2 Add '-1x2y' to each side of the equation. x2y + 2x3 + -1x2y + -2y3 = xy2 + -1x2y Reorder the terms: x2y + -1x2y + 2x3 + -2y3 = xy2 + -1x2y Combine like terms: x2y + -1x2y = 0 0 + 2x3 + -2y3 = xy2 + -1x2y 2x3 + -2y3 = xy2 + -1x2y Add '-2x3' to each side of the equation. 2x3 + -2x3 + -2y3 = xy2 + -1x2y + -2x3 Combine like terms: 2x3 + -2x3 = 0 0 + -2y3 = xy2 + -1x2y + -2x3 -2y3 = xy2 + -1x2y + -2x3 Add '2y3' to each side of the equation. -2y3 + 2y3 = xy2 + -1x2y + -2x3 + 2y3 Combine like terms: -2y3 + 2y3 = 0 0 = xy2 + -1x2y + -2x3 + 2y3 Simplifying 0 = xy2 + -1x2y + -2x3 + 2y3 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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