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Simplifying 3a(3a + -1)(3a + 5) = 0 Reorder the terms: 3a(-1 + 3a)(3a + 5) = 0 Reorder the terms: 3a(-1 + 3a)(5 + 3a) = 0 Multiply (-1 + 3a) * (5 + 3a) 3a(-1(5 + 3a) + 3a * (5 + 3a)) = 0 3a((5 * -1 + 3a * -1) + 3a * (5 + 3a)) = 0 3a((-5 + -3a) + 3a * (5 + 3a)) = 0 3a(-5 + -3a + (5 * 3a + 3a * 3a)) = 0 3a(-5 + -3a + (15a + 9a2)) = 0 Combine like terms: -3a + 15a = 12a 3a(-5 + 12a + 9a2) = 0 (-5 * 3a + 12a * 3a + 9a2 * 3a) = 0 (-15a + 36a2 + 27a3) = 0 Solving -15a + 36a2 + 27a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3a'. 3a(-5 + 12a + 9a2) = 0 Factor a trinomial. 3a((-5 + -3a)(1 + -3a)) = 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 '(-5 + -3a)' equal to zero and attempt to solve: Simplifying -5 + -3a = 0 Solving -5 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -3a = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3a = 0 + 5 -3a = 0 + 5 Combine like terms: 0 + 5 = 5 -3a = 5 Divide each side by '-3'. a = -1.666666667 Simplifying a = -1.666666667Subproblem 3
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 = 0.3333333333Solution
a = {0, -1.666666667, 0.3333333333}
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