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Simplifying (3xy + y2) * dx(x2 + xy) * dy = 0 Reorder the terms: (3xy + y2) * dx(xy + x2) * dy = 0 Reorder the terms for easier multiplication: dx * dy(3xy + y2)(xy + x2) = 0 Multiply dx * dy d2xy(3xy + y2)(xy + x2) = 0 Multiply (3xy + y2) * (xy + x2) d2xy(3xy * (xy + x2) + y2(xy + x2)) = 0 d2xy((xy * 3xy + x2 * 3xy) + y2(xy + x2)) = 0 d2xy((3x2y2 + 3x3y) + y2(xy + x2)) = 0 d2xy(3x2y2 + 3x3y + (xy * y2 + x2 * y2)) = 0 d2xy(3x2y2 + 3x3y + (xy3 + x2y2)) = 0 Reorder the terms: d2xy(xy3 + 3x2y2 + x2y2 + 3x3y) = 0 Combine like terms: 3x2y2 + x2y2 = 4x2y2 d2xy(xy3 + 4x2y2 + 3x3y) = 0 (xy3 * d2xy + 4x2y2 * d2xy + 3x3y * d2xy) = 0 (d2x2y4 + 4d2x3y3 + 3d2x4y2) = 0 Solving d2x2y4 + 4d2x3y3 + 3d2x4y2 = 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), 'd2x2y2'. d2x2y2(y2 + 4xy + 3x2) = 0 Factor a trinomial. d2x2y2((y + x)(y + 3x)) = 0Subproblem 1
Set the factor 'd2x2y2' equal to zero and attempt to solve: Simplifying d2x2y2 = 0 Solving d2x2y2 = 0 Move all terms containing d to the left, all other terms to the right. Simplifying d2x2y2 = 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 + 3x)' equal to zero and attempt to solve: Simplifying y + 3x = 0 Reorder the terms: 3x + y = 0 Solving 3x + y = 0 Move all terms containing d to the left, all other terms to the right. Add '-3x' to each side of the equation. 3x + -3x + y = 0 + -3x Combine like terms: 3x + -3x = 0 0 + y = 0 + -3x y = 0 + -3x Remove the zero: y = -3x Add '-1y' to each side of the equation. y + -1y = -3x + -1y Combine like terms: y + -1y = 0 0 = -3x + -1y Simplifying 0 = -3x + -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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