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Simplifying a(a + 4)(a + 8)(a + 12) = 585 Reorder the terms: a(4 + a)(a + 8)(a + 12) = 585 Reorder the terms: a(4 + a)(8 + a)(a + 12) = 585 Reorder the terms: a(4 + a)(8 + a)(12 + a) = 585 Multiply (4 + a) * (8 + a) a(4(8 + a) + a(8 + a))(12 + a) = 585 a((8 * 4 + a * 4) + a(8 + a))(12 + a) = 585 a((32 + 4a) + a(8 + a))(12 + a) = 585 a(32 + 4a + (8 * a + a * a))(12 + a) = 585 a(32 + 4a + (8a + a2))(12 + a) = 585 Combine like terms: 4a + 8a = 12a a(32 + 12a + a2)(12 + a) = 585 Multiply (32 + 12a + a2) * (12 + a) a(32(12 + a) + 12a * (12 + a) + a2(12 + a)) = 585 a((12 * 32 + a * 32) + 12a * (12 + a) + a2(12 + a)) = 585 a((384 + 32a) + 12a * (12 + a) + a2(12 + a)) = 585 a(384 + 32a + (12 * 12a + a * 12a) + a2(12 + a)) = 585 a(384 + 32a + (144a + 12a2) + a2(12 + a)) = 585 a(384 + 32a + 144a + 12a2 + (12 * a2 + a * a2)) = 585 a(384 + 32a + 144a + 12a2 + (12a2 + a3)) = 585 Combine like terms: 32a + 144a = 176a a(384 + 176a + 12a2 + 12a2 + a3) = 585 Combine like terms: 12a2 + 12a2 = 24a2 a(384 + 176a + 24a2 + a3) = 585 (384 * a + 176a * a + 24a2 * a + a3 * a) = 585 (384a + 176a2 + 24a3 + a4) = 585 Solving 384a + 176a2 + 24a3 + a4 = 585 Solving for variable 'a'. Reorder the terms: -585 + 384a + 176a2 + 24a3 + a4 = 585 + -585 Combine like terms: 585 + -585 = 0 -585 + 384a + 176a2 + 24a3 + a4 = 0 The solution to this equation could not be determined.
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