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