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Simplifying 3(a + 2)(a + 2) + 3(a + -1) + -27 = 0 Reorder the terms: 3(2 + a)(a + 2) + 3(a + -1) + -27 = 0 Reorder the terms: 3(2 + a)(2 + a) + 3(a + -1) + -27 = 0 Multiply (2 + a) * (2 + a) 3(2(2 + a) + a(2 + a)) + 3(a + -1) + -27 = 0 3((2 * 2 + a * 2) + a(2 + a)) + 3(a + -1) + -27 = 0 3((4 + 2a) + a(2 + a)) + 3(a + -1) + -27 = 0 3(4 + 2a + (2 * a + a * a)) + 3(a + -1) + -27 = 0 3(4 + 2a + (2a + a2)) + 3(a + -1) + -27 = 0 Combine like terms: 2a + 2a = 4a 3(4 + 4a + a2) + 3(a + -1) + -27 = 0 (4 * 3 + 4a * 3 + a2 * 3) + 3(a + -1) + -27 = 0 (12 + 12a + 3a2) + 3(a + -1) + -27 = 0 Reorder the terms: 12 + 12a + 3a2 + 3(-1 + a) + -27 = 0 12 + 12a + 3a2 + (-1 * 3 + a * 3) + -27 = 0 12 + 12a + 3a2 + (-3 + 3a) + -27 = 0 Reorder the terms: 12 + -3 + -27 + 12a + 3a + 3a2 = 0 Combine like terms: 12 + -3 = 9 9 + -27 + 12a + 3a + 3a2 = 0 Combine like terms: 9 + -27 = -18 -18 + 12a + 3a + 3a2 = 0 Combine like terms: 12a + 3a = 15a -18 + 15a + 3a2 = 0 Solving -18 + 15a + 3a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3'. 3(-6 + 5a + a2) = 0 Factor a trinomial. 3((-6 + -1a)(1 + -1a)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-6 + -1a)' equal to zero and attempt to solve: Simplifying -6 + -1a = 0 Solving -6 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1a = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1a = 0 + 6 -1a = 0 + 6 Combine like terms: 0 + 6 = 6 -1a = 6 Divide each side by '-1'. a = -6 Simplifying a = -6Subproblem 2
Set the factor '(1 + -1a)' equal to zero and attempt to solve: Simplifying 1 + -1a = 0 Solving 1 + -1a = 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 + -1a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1a = 0 + -1 -1a = 0 + -1 Combine like terms: 0 + -1 = -1 -1a = -1 Divide each side by '-1'. a = 1 Simplifying a = 1Solution
a = {-6, 1}
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