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Simplifying 3a2 + 21 = -24a Reorder the terms: 21 + 3a2 = -24a Solving 21 + 3a2 = -24a Solving for variable 'a'. Reorder the terms: 21 + 24a + 3a2 = -24a + 24a Combine like terms: -24a + 24a = 0 21 + 24a + 3a2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(7 + 8a + a2) = 0 Factor a trinomial. 3((7 + a)(1 + a)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(7 + a)' equal to zero and attempt to solve: Simplifying 7 + a = 0 Solving 7 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + a = 0 + -7 a = 0 + -7 Combine like terms: 0 + -7 = -7 a = -7 Simplifying a = -7Subproblem 2
Set the factor '(1 + a)' equal to zero and attempt to solve: Simplifying 1 + a = 0 Solving 1 + a = 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 + a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + a = 0 + -1 a = 0 + -1 Combine like terms: 0 + -1 = -1 a = -1 Simplifying a = -1Solution
a = {-7, -1}
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