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Simplifying (5 + u)(3u + 7) = 0 Reorder the terms: (5 + u)(7 + 3u) = 0 Multiply (5 + u) * (7 + 3u) (5(7 + 3u) + u(7 + 3u)) = 0 ((7 * 5 + 3u * 5) + u(7 + 3u)) = 0 ((35 + 15u) + u(7 + 3u)) = 0 (35 + 15u + (7 * u + 3u * u)) = 0 (35 + 15u + (7u + 3u2)) = 0 Combine like terms: 15u + 7u = 22u (35 + 22u + 3u2) = 0 Solving 35 + 22u + 3u2 = 0 Solving for variable 'u'. Factor a trinomial. (5 + u)(7 + 3u) = 0Subproblem 1
Set the factor '(5 + u)' equal to zero and attempt to solve: Simplifying 5 + u = 0 Solving 5 + u = 0 Move all terms containing u to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + u = 0 + -5 Combine like terms: 5 + -5 = 0 0 + u = 0 + -5 u = 0 + -5 Combine like terms: 0 + -5 = -5 u = -5 Simplifying u = -5Subproblem 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 = {-5, -2.333333333}
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