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Simplifying -3a(3a + 1)(a + -4) = 0 Reorder the terms: -3a(1 + 3a)(a + -4) = 0 Reorder the terms: -3a(1 + 3a)(-4 + a) = 0 Multiply (1 + 3a) * (-4 + a) -3a(1(-4 + a) + 3a * (-4 + a)) = 0 -3a((-4 * 1 + a * 1) + 3a * (-4 + a)) = 0 -3a((-4 + 1a) + 3a * (-4 + a)) = 0 -3a(-4 + 1a + (-4 * 3a + a * 3a)) = 0 -3a(-4 + 1a + (-12a + 3a2)) = 0 Combine like terms: 1a + -12a = -11a -3a(-4 + -11a + 3a2) = 0 (-4 * -3a + -11a * -3a + 3a2 * -3a) = 0 (12a + 33a2 + -9a3) = 0 Solving 12a + 33a2 + -9a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3a'. 3a(4 + 11a + -3a2) = 0 Factor a trinomial. 3a((4 + -1a)(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 '(4 + -1a)' equal to zero and attempt to solve: Simplifying 4 + -1a = 0 Solving 4 + -1a = 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 + -1a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1a = 0 + -4 -1a = 0 + -4 Combine like terms: 0 + -4 = -4 -1a = -4 Divide each side by '-1'. a = 4 Simplifying a = 4Subproblem 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, 4, -0.3333333333}
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