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Simplifying 2a(a + 3)(8a + -3) = 0 Reorder the terms: 2a(3 + a)(8a + -3) = 0 Reorder the terms: 2a(3 + a)(-3 + 8a) = 0 Multiply (3 + a) * (-3 + 8a) 2a(3(-3 + 8a) + a(-3 + 8a)) = 0 2a((-3 * 3 + 8a * 3) + a(-3 + 8a)) = 0 2a((-9 + 24a) + a(-3 + 8a)) = 0 2a(-9 + 24a + (-3 * a + 8a * a)) = 0 2a(-9 + 24a + (-3a + 8a2)) = 0 Combine like terms: 24a + -3a = 21a 2a(-9 + 21a + 8a2) = 0 (-9 * 2a + 21a * 2a + 8a2 * 2a) = 0 (-18a + 42a2 + 16a3) = 0 Solving -18a + 42a2 + 16a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2a'. 2a(-9 + 21a + 8a2) = 0 Factor a trinomial. 2a((-3 + -1a)(3 + -8a)) = 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 '(-3 + -1a)' equal to zero and attempt to solve: Simplifying -3 + -1a = 0 Solving -3 + -1a = 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 + -1a = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1a = 0 + 3 -1a = 0 + 3 Combine like terms: 0 + 3 = 3 -1a = 3 Divide each side by '-1'. a = -3 Simplifying a = -3Subproblem 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, -3, 0.375}
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