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Simplifying (a + 4)(-8a + 16) = 0 Reorder the terms: (4 + a)(-8a + 16) = 0 Reorder the terms: (4 + a)(16 + -8a) = 0 Multiply (4 + a) * (16 + -8a) (4(16 + -8a) + a(16 + -8a)) = 0 ((16 * 4 + -8a * 4) + a(16 + -8a)) = 0 ((64 + -32a) + a(16 + -8a)) = 0 (64 + -32a + (16 * a + -8a * a)) = 0 (64 + -32a + (16a + -8a2)) = 0 Combine like terms: -32a + 16a = -16a (64 + -16a + -8a2) = 0 Solving 64 + -16a + -8a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '8'. 8(8 + -2a + -1a2) = 0 Factor a trinomial. 8((2 + -1a)(4 + a)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(2 + -1a)' equal to zero and attempt to solve: Simplifying 2 + -1a = 0 Solving 2 + -1a = 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 + -1a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1a = 0 + -2 -1a = 0 + -2 Combine like terms: 0 + -2 = -2 -1a = -2 Divide each side by '-1'. a = 2 Simplifying a = 2Subproblem 2
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 = -4Solution
a = {2, -4}
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