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Simplifying 2a(4a + -1)(3a + 9) = 0 Reorder the terms: 2a(-1 + 4a)(3a + 9) = 0 Reorder the terms: 2a(-1 + 4a)(9 + 3a) = 0 Multiply (-1 + 4a) * (9 + 3a) 2a(-1(9 + 3a) + 4a * (9 + 3a)) = 0 2a((9 * -1 + 3a * -1) + 4a * (9 + 3a)) = 0 2a((-9 + -3a) + 4a * (9 + 3a)) = 0 2a(-9 + -3a + (9 * 4a + 3a * 4a)) = 0 2a(-9 + -3a + (36a + 12a2)) = 0 Combine like terms: -3a + 36a = 33a 2a(-9 + 33a + 12a2) = 0 (-9 * 2a + 33a * 2a + 12a2 * 2a) = 0 (-18a + 66a2 + 24a3) = 0 Solving -18a + 66a2 + 24a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '6a'. 6a(-3 + 11a + 4a2) = 0 Factor a trinomial. 6a((-3 + -1a)(1 + -4a)) = 0 Ignore the factor 6.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 '(1 + -4a)' equal to zero and attempt to solve: Simplifying 1 + -4a = 0 Solving 1 + -4a = 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 + -4a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4a = 0 + -1 -4a = 0 + -1 Combine like terms: 0 + -1 = -1 -4a = -1 Divide each side by '-4'. a = 0.25 Simplifying a = 0.25Solution
a = {0, -3, 0.25}
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