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Simplifying (3y2 + 3xy + x2) * dx = (x2 + 2xy) * dy Reorder the terms: (3xy + x2 + 3y2) * dx = (x2 + 2xy) * dy Reorder the terms for easier multiplication: dx(3xy + x2 + 3y2) = (x2 + 2xy) * dy (3xy * dx + x2 * dx + 3y2 * dx) = (x2 + 2xy) * dy Reorder the terms: (3dxy2 + 3dx2y + dx3) = (x2 + 2xy) * dy (3dxy2 + 3dx2y + dx3) = (x2 + 2xy) * dy Reorder the terms: 3dxy2 + 3dx2y + dx3 = (2xy + x2) * dy Reorder the terms for easier multiplication: 3dxy2 + 3dx2y + dx3 = dy(2xy + x2) 3dxy2 + 3dx2y + dx3 = (2xy * dy + x2 * dy) 3dxy2 + 3dx2y + dx3 = (2dxy2 + dx2y) Solving 3dxy2 + 3dx2y + dx3 = 2dxy2 + dx2y Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-2dxy2' to each side of the equation. 3dxy2 + 3dx2y + -2dxy2 + dx3 = 2dxy2 + -2dxy2 + dx2y Reorder the terms: 3dxy2 + -2dxy2 + 3dx2y + dx3 = 2dxy2 + -2dxy2 + dx2y Combine like terms: 3dxy2 + -2dxy2 = 1dxy2 1dxy2 + 3dx2y + dx3 = 2dxy2 + -2dxy2 + dx2y Combine like terms: 2dxy2 + -2dxy2 = 0 1dxy2 + 3dx2y + dx3 = 0 + dx2y 1dxy2 + 3dx2y + dx3 = dx2y Add '-1dx2y' to each side of the equation. 1dxy2 + 3dx2y + -1dx2y + dx3 = dx2y + -1dx2y Combine like terms: 3dx2y + -1dx2y = 2dx2y 1dxy2 + 2dx2y + dx3 = dx2y + -1dx2y Combine like terms: dx2y + -1dx2y = 0 1dxy2 + 2dx2y + dx3 = 0 Factor out the Greatest Common Factor (GCF), 'dx'. dx(y2 + 2xy + x2) = 0 Factor a trinomial. dx((y + x)(y + x)) = 0Subproblem 1
Set the factor 'dx' equal to zero and attempt to solve: Simplifying dx = 0 Solving dx = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dx = 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 '(y + x)' equal to zero and attempt to solve: Simplifying y + x = 0 Reorder the terms: x + y = 0 Solving x + y = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x + y = 0 + -1x Combine like terms: x + -1x = 0 0 + y = 0 + -1x y = 0 + -1x Remove the zero: y = -1x Add '-1y' to each side of the equation. y + -1y = -1x + -1y Combine like terms: y + -1y = 0 0 = -1x + -1y Simplifying 0 = -1x + -1y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(y + x)' equal to zero and attempt to solve: Simplifying y + x = 0 Reorder the terms: x + y = 0 Solving x + y = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x + y = 0 + -1x Combine like terms: x + -1x = 0 0 + y = 0 + -1x y = 0 + -1x Remove the zero: y = -1x Add '-1y' to each side of the equation. y + -1y = -1x + -1y Combine like terms: y + -1y = 0 0 = -1x + -1y Simplifying 0 = -1x + -1y 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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