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Simplifying 2a(3a + 4)(3a + 4) = 0 Reorder the terms: 2a(4 + 3a)(3a + 4) = 0 Reorder the terms: 2a(4 + 3a)(4 + 3a) = 0 Multiply (4 + 3a) * (4 + 3a) 2a(4(4 + 3a) + 3a * (4 + 3a)) = 0 2a((4 * 4 + 3a * 4) + 3a * (4 + 3a)) = 0 2a((16 + 12a) + 3a * (4 + 3a)) = 0 2a(16 + 12a + (4 * 3a + 3a * 3a)) = 0 2a(16 + 12a + (12a + 9a2)) = 0 Combine like terms: 12a + 12a = 24a 2a(16 + 24a + 9a2) = 0 (16 * 2a + 24a * 2a + 9a2 * 2a) = 0 (32a + 48a2 + 18a3) = 0 Solving 32a + 48a2 + 18a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2a'. 2a(16 + 24a + 9a2) = 0 Factor a trinomial. 2a((4 + 3a)(4 + 3a)) = 0 Ignore the factor 2.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 '(4 + 3a)' equal to zero and attempt to solve: Simplifying 4 + 3a = 0 Solving 4 + 3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 3a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3a = 0 + -4 3a = 0 + -4 Combine like terms: 0 + -4 = -4 3a = -4 Divide each side by '3'. a = -1.333333333 Simplifying a = -1.333333333Subproblem 3
Set the factor '(4 + 3a)' equal to zero and attempt to solve: Simplifying 4 + 3a = 0 Solving 4 + 3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 3a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3a = 0 + -4 3a = 0 + -4 Combine like terms: 0 + -4 = -4 3a = -4 Divide each side by '3'. a = -1.333333333 Simplifying a = -1.333333333Solution
a = {0, -1.333333333, -1.333333333}
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