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Simplifying (3u + 7)(6 + u) = 0 Reorder the terms: (7 + 3u)(6 + u) = 0 Multiply (7 + 3u) * (6 + u) (7(6 + u) + 3u * (6 + u)) = 0 ((6 * 7 + u * 7) + 3u * (6 + u)) = 0 ((42 + 7u) + 3u * (6 + u)) = 0 (42 + 7u + (6 * 3u + u * 3u)) = 0 (42 + 7u + (18u + 3u2)) = 0 Combine like terms: 7u + 18u = 25u (42 + 25u + 3u2) = 0 Solving 42 + 25u + 3u2 = 0 Solving for variable 'u'. Factor a trinomial. (6 + u)(7 + 3u) = 0Subproblem 1
Set the factor '(6 + u)' equal to zero and attempt to solve: Simplifying 6 + u = 0 Solving 6 + u = 0 Move all terms containing u to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + u = 0 + -6 Combine like terms: 6 + -6 = 0 0 + u = 0 + -6 u = 0 + -6 Combine like terms: 0 + -6 = -6 u = -6 Simplifying u = -6Subproblem 2
Set the factor '(7 + 3u)' equal to zero and attempt to solve: Simplifying 7 + 3u = 0 Solving 7 + 3u = 0 Move all terms containing u to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 3u = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3u = 0 + -7 3u = 0 + -7 Combine like terms: 0 + -7 = -7 3u = -7 Divide each side by '3'. u = -2.333333333 Simplifying u = -2.333333333Solution
u = {-6, -2.333333333}
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