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Simplifying 0 = a2 + 7a + 12 Reorder the terms: 0 = 12 + 7a + a2 Solving 0 = 12 + 7a + a2 Solving for variable 'a'. Combine like terms: 0 + -12 = -12 -12 + -7a + -1a2 = 12 + 7a + a2 + -12 + -7a + -1a2 Reorder the terms: -12 + -7a + -1a2 = 12 + -12 + 7a + -7a + a2 + -1a2 Combine like terms: 12 + -12 = 0 -12 + -7a + -1a2 = 0 + 7a + -7a + a2 + -1a2 -12 + -7a + -1a2 = 7a + -7a + a2 + -1a2 Combine like terms: 7a + -7a = 0 -12 + -7a + -1a2 = 0 + a2 + -1a2 -12 + -7a + -1a2 = a2 + -1a2 Combine like terms: a2 + -1a2 = 0 -12 + -7a + -1a2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(12 + 7a + a2) = 0 Factor a trinomial. -1((4 + a)(3 + a)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + a)' equal to zero and attempt to solve: Simplifying 4 + a = 0 Solving 4 + a = 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 + a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + a = 0 + -4 a = 0 + -4 Combine like terms: 0 + -4 = -4 a = -4 Simplifying a = -4Subproblem 2
Set the factor '(3 + a)' equal to zero and attempt to solve: Simplifying 3 + a = 0 Solving 3 + a = 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 + a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + a = 0 + -3 a = 0 + -3 Combine like terms: 0 + -3 = -3 a = -3 Simplifying a = -3Solution
a = {-4, -3}
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