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Simplifying (3x2 + 2y2) * dx(4xy + 6y2) * dy = 0 Reorder the terms for easier multiplication: dx * dy(3x2 + 2y2)(4xy + 6y2) = 0 Multiply dx * dy d2xy(3x2 + 2y2)(4xy + 6y2) = 0 Multiply (3x2 + 2y2) * (4xy + 6y2) d2xy(3x2 * (4xy + 6y2) + 2y2 * (4xy + 6y2)) = 0 d2xy((4xy * 3x2 + 6y2 * 3x2) + 2y2 * (4xy + 6y2)) = 0 Reorder the terms: d2xy((18x2y2 + 12x3y) + 2y2 * (4xy + 6y2)) = 0 d2xy((18x2y2 + 12x3y) + 2y2 * (4xy + 6y2)) = 0 d2xy(18x2y2 + 12x3y + (4xy * 2y2 + 6y2 * 2y2)) = 0 d2xy(18x2y2 + 12x3y + (8xy3 + 12y4)) = 0 Reorder the terms: d2xy(8xy3 + 18x2y2 + 12x3y + 12y4) = 0 d2xy(8xy3 + 18x2y2 + 12x3y + 12y4) = 0 (8xy3 * d2xy + 18x2y2 * d2xy + 12x3y * d2xy + 12y4 * d2xy) = 0 Reorder the terms: (12d2xy5 + 8d2x2y4 + 18d2x3y3 + 12d2x4y2) = 0 (12d2xy5 + 8d2x2y4 + 18d2x3y3 + 12d2x4y2) = 0 Solving 12d2xy5 + 8d2x2y4 + 18d2x3y3 + 12d2x4y2 = 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), '2d2xy2'. 2d2xy2(6y3 + 4xy2 + 9x2y + 6x3) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'd2xy2' equal to zero and attempt to solve: Simplifying d2xy2 = 0 Solving d2xy2 = 0 Move all terms containing d to the left, all other terms to the right. Simplifying d2xy2 = 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 '(6y3 + 4xy2 + 9x2y + 6x3)' equal to zero and attempt to solve: Simplifying 6y3 + 4xy2 + 9x2y + 6x3 = 0 Reorder the terms: 4xy2 + 9x2y + 6x3 + 6y3 = 0 Solving 4xy2 + 9x2y + 6x3 + 6y3 = 0 Move all terms containing d to the left, all other terms to the right. Add '-4xy2' to each side of the equation. 4xy2 + 9x2y + 6x3 + -4xy2 + 6y3 = 0 + -4xy2 Reorder the terms: 4xy2 + -4xy2 + 9x2y + 6x3 + 6y3 = 0 + -4xy2 Combine like terms: 4xy2 + -4xy2 = 0 0 + 9x2y + 6x3 + 6y3 = 0 + -4xy2 9x2y + 6x3 + 6y3 = 0 + -4xy2 Remove the zero: 9x2y + 6x3 + 6y3 = -4xy2 Add '-9x2y' to each side of the equation. 9x2y + 6x3 + -9x2y + 6y3 = -4xy2 + -9x2y Reorder the terms: 9x2y + -9x2y + 6x3 + 6y3 = -4xy2 + -9x2y Combine like terms: 9x2y + -9x2y = 0 0 + 6x3 + 6y3 = -4xy2 + -9x2y 6x3 + 6y3 = -4xy2 + -9x2y Add '-6x3' to each side of the equation. 6x3 + -6x3 + 6y3 = -4xy2 + -9x2y + -6x3 Combine like terms: 6x3 + -6x3 = 0 0 + 6y3 = -4xy2 + -9x2y + -6x3 6y3 = -4xy2 + -9x2y + -6x3 Add '-6y3' to each side of the equation. 6y3 + -6y3 = -4xy2 + -9x2y + -6x3 + -6y3 Combine like terms: 6y3 + -6y3 = 0 0 = -4xy2 + -9x2y + -6x3 + -6y3 Simplifying 0 = -4xy2 + -9x2y + -6x3 + -6y3 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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