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Simplifying (3u + 1)(8 + u) = 0 Reorder the terms: (1 + 3u)(8 + u) = 0 Multiply (1 + 3u) * (8 + u) (1(8 + u) + 3u * (8 + u)) = 0 ((8 * 1 + u * 1) + 3u * (8 + u)) = 0 ((8 + 1u) + 3u * (8 + u)) = 0 (8 + 1u + (8 * 3u + u * 3u)) = 0 (8 + 1u + (24u + 3u2)) = 0 Combine like terms: 1u + 24u = 25u (8 + 25u + 3u2) = 0 Solving 8 + 25u + 3u2 = 0 Solving for variable 'u'. Factor a trinomial. (8 + u)(1 + 3u) = 0Subproblem 1
Set the factor '(8 + u)' equal to zero and attempt to solve: Simplifying 8 + u = 0 Solving 8 + u = 0 Move all terms containing u to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + u = 0 + -8 Combine like terms: 8 + -8 = 0 0 + u = 0 + -8 u = 0 + -8 Combine like terms: 0 + -8 = -8 u = -8 Simplifying u = -8Subproblem 2
Set the factor '(1 + 3u)' equal to zero and attempt to solve: Simplifying 1 + 3u = 0 Solving 1 + 3u = 0 Move all terms containing u to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 3u = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3u = 0 + -1 3u = 0 + -1 Combine like terms: 0 + -1 = -1 3u = -1 Divide each side by '3'. u = -0.3333333333 Simplifying u = -0.3333333333Solution
u = {-8, -0.3333333333}
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