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Simplifying 3a(8a + -3)(3a + -1) = 0 Reorder the terms: 3a(-3 + 8a)(3a + -1) = 0 Reorder the terms: 3a(-3 + 8a)(-1 + 3a) = 0 Multiply (-3 + 8a) * (-1 + 3a) 3a(-3(-1 + 3a) + 8a * (-1 + 3a)) = 0 3a((-1 * -3 + 3a * -3) + 8a * (-1 + 3a)) = 0 3a((3 + -9a) + 8a * (-1 + 3a)) = 0 3a(3 + -9a + (-1 * 8a + 3a * 8a)) = 0 3a(3 + -9a + (-8a + 24a2)) = 0 Combine like terms: -9a + -8a = -17a 3a(3 + -17a + 24a2) = 0 (3 * 3a + -17a * 3a + 24a2 * 3a) = 0 (9a + -51a2 + 72a3) = 0 Solving 9a + -51a2 + 72a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3a'. 3a(3 + -17a + 24a2) = 0 Factor a trinomial. 3a((1 + -3a)(3 + -8a)) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(1 + -3a)' equal to zero and attempt to solve: Simplifying 1 + -3a = 0 Solving 1 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3a = 0 + -1 -3a = 0 + -1 Combine like terms: 0 + -1 = -1 -3a = -1 Divide each side by '-3'. a = 0.3333333333 Simplifying a = 0.3333333333Subproblem 3
Set the factor '(3 + -8a)' equal to zero and attempt to solve: Simplifying 3 + -8a = 0 Solving 3 + -8a = 0 Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -8a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8a = 0 + -3 -8a = 0 + -3 Combine like terms: 0 + -3 = -3 -8a = -3 Divide each side by '-8'. a = 0.375 Simplifying a = 0.375Solution
a = {0, 0.3333333333, 0.375}
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