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Simplifying (2y3 + 2y2) * dx(3y2x + 2xy) * dy = 0 Reorder the terms: (2y2 + 2y3) * dx(3y2x + 2xy) * dy = 0 Reorder the terms: (2y2 + 2y3) * dx(2xy + 3xy2) * dy = 0 Reorder the terms for easier multiplication: dx * dy(2y2 + 2y3)(2xy + 3xy2) = 0 Multiply dx * dy d2xy(2y2 + 2y3)(2xy + 3xy2) = 0 Multiply (2y2 + 2y3) * (2xy + 3xy2) d2xy(2y2 * (2xy + 3xy2) + 2y3 * (2xy + 3xy2)) = 0 d2xy((2xy * 2y2 + 3xy2 * 2y2) + 2y3 * (2xy + 3xy2)) = 0 d2xy((4xy3 + 6xy4) + 2y3 * (2xy + 3xy2)) = 0 d2xy(4xy3 + 6xy4 + (2xy * 2y3 + 3xy2 * 2y3)) = 0 d2xy(4xy3 + 6xy4 + (4xy4 + 6xy5)) = 0 Combine like terms: 6xy4 + 4xy4 = 10xy4 d2xy(4xy3 + 10xy4 + 6xy5) = 0 (4xy3 * d2xy + 10xy4 * d2xy + 6xy5 * d2xy) = 0 (4d2x2y4 + 10d2x2y5 + 6d2x2y6) = 0 Solving 4d2x2y4 + 10d2x2y5 + 6d2x2y6 = 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), '2d2x2y4'. 2d2x2y4(2 + 5y + 3y2) = 0 Factor a trinomial. 2d2x2y4((1 + y)(2 + 3y)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'd2x2y4' equal to zero and attempt to solve: Simplifying d2x2y4 = 0 Solving d2x2y4 = 0 Move all terms containing d to the left, all other terms to the right. Simplifying d2x2y4 = 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 '(1 + y)' equal to zero and attempt to solve: Simplifying 1 + y = 0 Solving 1 + y = 0 Move all terms containing d to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + y = 0 + -1 y = 0 + -1 Combine like terms: 0 + -1 = -1 y = -1 Add '-1y' to each side of the equation. y + -1y = -1 + -1y Combine like terms: y + -1y = 0 0 = -1 + -1y Simplifying 0 = -1 + -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 '(2 + 3y)' equal to zero and attempt to solve: Simplifying 2 + 3y = 0 Solving 2 + 3y = 0 Move all terms containing d to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 3y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3y = 0 + -2 3y = 0 + -2 Combine like terms: 0 + -2 = -2 3y = -2 Add '-3y' to each side of the equation. 3y + -3y = -2 + -3y Combine like terms: 3y + -3y = 0 0 = -2 + -3y Simplifying 0 = -2 + -3y 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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