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Simplifying 27a2 + 216a + 128 = 8a + 3a2 Reorder the terms: 128 + 216a + 27a2 = 8a + 3a2 Solving 128 + 216a + 27a2 = 8a + 3a2 Solving for variable 'a'. Reorder the terms: 128 + 216a + -8a + 27a2 + -3a2 = 8a + 3a2 + -8a + -3a2 Combine like terms: 216a + -8a = 208a 128 + 208a + 27a2 + -3a2 = 8a + 3a2 + -8a + -3a2 Combine like terms: 27a2 + -3a2 = 24a2 128 + 208a + 24a2 = 8a + 3a2 + -8a + -3a2 Reorder the terms: 128 + 208a + 24a2 = 8a + -8a + 3a2 + -3a2 Combine like terms: 8a + -8a = 0 128 + 208a + 24a2 = 0 + 3a2 + -3a2 128 + 208a + 24a2 = 3a2 + -3a2 Combine like terms: 3a2 + -3a2 = 0 128 + 208a + 24a2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(16 + 26a + 3a2) = 0 Factor a trinomial. 8((8 + a)(2 + 3a)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(8 + a)' equal to zero and attempt to solve: Simplifying 8 + a = 0 Solving 8 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + a = 0 + -8 Combine like terms: 8 + -8 = 0 0 + a = 0 + -8 a = 0 + -8 Combine like terms: 0 + -8 = -8 a = -8 Simplifying a = -8Subproblem 2
Set the factor '(2 + 3a)' equal to zero and attempt to solve: Simplifying 2 + 3a = 0 Solving 2 + 3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 3a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3a = 0 + -2 3a = 0 + -2 Combine like terms: 0 + -2 = -2 3a = -2 Divide each side by '3'. a = -0.6666666667 Simplifying a = -0.6666666667Solution
a = {-8, -0.6666666667}
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