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Simplifying (3u + -7)(5 + u) = 0 Reorder the terms: (-7 + 3u)(5 + u) = 0 Multiply (-7 + 3u) * (5 + u) (-7(5 + u) + 3u * (5 + u)) = 0 ((5 * -7 + u * -7) + 3u * (5 + u)) = 0 ((-35 + -7u) + 3u * (5 + u)) = 0 (-35 + -7u + (5 * 3u + u * 3u)) = 0 (-35 + -7u + (15u + 3u2)) = 0 Combine like terms: -7u + 15u = 8u (-35 + 8u + 3u2) = 0 Solving -35 + 8u + 3u2 = 0 Solving for variable 'u'. Factor a trinomial. (-5 + -1u)(7 + -3u) = 0Subproblem 1
Set the factor '(-5 + -1u)' equal to zero and attempt to solve: Simplifying -5 + -1u = 0 Solving -5 + -1u = 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 + -1u = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1u = 0 + 5 -1u = 0 + 5 Combine like terms: 0 + 5 = 5 -1u = 5 Divide each side by '-1'. 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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