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Simplifying (5 + u)(4u + 3) = 0 Reorder the terms: (5 + u)(3 + 4u) = 0 Multiply (5 + u) * (3 + 4u) (5(3 + 4u) + u(3 + 4u)) = 0 ((3 * 5 + 4u * 5) + u(3 + 4u)) = 0 ((15 + 20u) + u(3 + 4u)) = 0 (15 + 20u + (3 * u + 4u * u)) = 0 (15 + 20u + (3u + 4u2)) = 0 Combine like terms: 20u + 3u = 23u (15 + 23u + 4u2) = 0 Solving 15 + 23u + 4u2 = 0 Solving for variable 'u'. Factor a trinomial. (5 + u)(3 + 4u) = 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 '(3 + 4u)' equal to zero and attempt to solve: Simplifying 3 + 4u = 0 Solving 3 + 4u = 0 Move all terms containing u to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 4u = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4u = 0 + -3 4u = 0 + -3 Combine like terms: 0 + -3 = -3 4u = -3 Divide each side by '4'. u = -0.75 Simplifying u = -0.75Solution
u = {-5, -0.75}
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