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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 = 15 15 + -27 + 12a + -3a + 3a2 = 0 Combine like terms: 15 + -27 = -12 -12 + 12a + -3a + 3a2 = 0 Combine like terms: 12a + -3a = 9a -12 + 9a + 3a2 = 0 Solving -12 + 9a + 3a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + 3a + a2) = 0 Factor a trinomial. 3((-4 + -1a)(1 + -1a)) = 0 Ignore the factor 3.Subproblem 1
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 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 = {-4, 1}
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