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Simplifying (2a + 8)(8a + 2) = 0 Reorder the terms: (8 + 2a)(8a + 2) = 0 Reorder the terms: (8 + 2a)(2 + 8a) = 0 Multiply (8 + 2a) * (2 + 8a) (8(2 + 8a) + 2a * (2 + 8a)) = 0 ((2 * 8 + 8a * 8) + 2a * (2 + 8a)) = 0 ((16 + 64a) + 2a * (2 + 8a)) = 0 (16 + 64a + (2 * 2a + 8a * 2a)) = 0 (16 + 64a + (4a + 16a2)) = 0 Combine like terms: 64a + 4a = 68a (16 + 68a + 16a2) = 0 Solving 16 + 68a + 16a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4'. 4(4 + 17a + 4a2) = 0 Factor a trinomial. 4((4 + a)(1 + 4a)) = 0 Ignore the factor 4.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 '(1 + 4a)' equal to zero and attempt to solve: Simplifying 1 + 4a = 0 Solving 1 + 4a = 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 + 4a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4a = 0 + -1 4a = 0 + -1 Combine like terms: 0 + -1 = -1 4a = -1 Divide each side by '4'. a = -0.25 Simplifying a = -0.25Solution
a = {-4, -0.25}
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