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Simplifying (2a + -3b)(4a2 + 6ab + 9b2)(8a3 + 27b3) = 0 Reorder the terms: (2a + -3b)(6ab + 4a2 + 9b2)(8a3 + 27b3) = 0 Multiply (2a + -3b) * (6ab + 4a2 + 9b2) (2a * (6ab + 4a2 + 9b2) + -3b * (6ab + 4a2 + 9b2))(8a3 + 27b3) = 0 ((6ab * 2a + 4a2 * 2a + 9b2 * 2a) + -3b * (6ab + 4a2 + 9b2))(8a3 + 27b3) = 0 Reorder the terms: ((18ab2 + 12a2b + 8a3) + -3b * (6ab + 4a2 + 9b2))(8a3 + 27b3) = 0 ((18ab2 + 12a2b + 8a3) + -3b * (6ab + 4a2 + 9b2))(8a3 + 27b3) = 0 (18ab2 + 12a2b + 8a3 + (6ab * -3b + 4a2 * -3b + 9b2 * -3b))(8a3 + 27b3) = 0 (18ab2 + 12a2b + 8a3 + (-18ab2 + -12a2b + -27b3))(8a3 + 27b3) = 0 Reorder the terms: (18ab2 + -18ab2 + 12a2b + -12a2b + 8a3 + -27b3)(8a3 + 27b3) = 0 Combine like terms: 18ab2 + -18ab2 = 0 (0 + 12a2b + -12a2b + 8a3 + -27b3)(8a3 + 27b3) = 0 (12a2b + -12a2b + 8a3 + -27b3)(8a3 + 27b3) = 0 Combine like terms: 12a2b + -12a2b = 0 (0 + 8a3 + -27b3)(8a3 + 27b3) = 0 (8a3 + -27b3)(8a3 + 27b3) = 0 Multiply (8a3 + -27b3) * (8a3 + 27b3) (8a3 * (8a3 + 27b3) + -27b3 * (8a3 + 27b3)) = 0 ((8a3 * 8a3 + 27b3 * 8a3) + -27b3 * (8a3 + 27b3)) = 0 Reorder the terms: ((216a3b3 + 64a6) + -27b3 * (8a3 + 27b3)) = 0 ((216a3b3 + 64a6) + -27b3 * (8a3 + 27b3)) = 0 (216a3b3 + 64a6 + (8a3 * -27b3 + 27b3 * -27b3)) = 0 (216a3b3 + 64a6 + (-216a3b3 + -729b6)) = 0 Reorder the terms: (216a3b3 + -216a3b3 + 64a6 + -729b6) = 0 Combine like terms: 216a3b3 + -216a3b3 = 0 (0 + 64a6 + -729b6) = 0 (64a6 + -729b6) = 0 Solving 64a6 + -729b6 = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '729b6' to each side of the equation. 64a6 + -729b6 + 729b6 = 0 + 729b6 Combine like terms: -729b6 + 729b6 = 0 64a6 + 0 = 0 + 729b6 64a6 = 0 + 729b6 Remove the zero: 64a6 = 729b6 Divide each side by '64'. a6 = 11.390625b6 Simplifying a6 = 11.390625b6 Combine like terms: 11.390625b6 + -11.390625b6 = 0.000000 a6 + -11.390625b6 = 0.000000 Factor a difference between two squares. (a3 + 3.375b3)(a3 + -3.375b3) = 0.000000Subproblem 1
Set the factor '(a3 + 3.375b3)' equal to zero and attempt to solve: Simplifying a3 + 3.375b3 = 0 Solving a3 + 3.375b3 = 0 Move all terms containing a to the left, all other terms to the right. Add '-3.375b3' to each side of the equation. a3 + 3.375b3 + -3.375b3 = 0 + -3.375b3 Combine like terms: 3.375b3 + -3.375b3 = 0.000 a3 + 0.000 = 0 + -3.375b3 a3 = 0 + -3.375b3 Remove the zero: a3 = -3.375b3 Simplifying a3 = -3.375b3 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 '(a3 + -3.375b3)' equal to zero and attempt to solve: Simplifying a3 + -3.375b3 = 0 Solving a3 + -3.375b3 = 0 Move all terms containing a to the left, all other terms to the right. Add '3.375b3' to each side of the equation. a3 + -3.375b3 + 3.375b3 = 0 + 3.375b3 Combine like terms: -3.375b3 + 3.375b3 = 0.000 a3 + 0.000 = 0 + 3.375b3 a3 = 0 + 3.375b3 Remove the zero: a3 = 3.375b3 Simplifying a3 = 3.375b3 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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