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Simplifying 2(u + 2) = -6(u + 2)(u + 1) + (u + 1) Reorder the terms: 2(2 + u) = -6(u + 2)(u + 1) + (u + 1) (2 * 2 + u * 2) = -6(u + 2)(u + 1) + (u + 1) (4 + 2u) = -6(u + 2)(u + 1) + (u + 1) Reorder the terms: 4 + 2u = -6(2 + u)(u + 1) + (u + 1) Reorder the terms: 4 + 2u = -6(2 + u)(1 + u) + (u + 1) Multiply (2 + u) * (1 + u) 4 + 2u = -6(2(1 + u) + u(1 + u)) + (u + 1) 4 + 2u = -6((1 * 2 + u * 2) + u(1 + u)) + (u + 1) 4 + 2u = -6((2 + 2u) + u(1 + u)) + (u + 1) 4 + 2u = -6(2 + 2u + (1 * u + u * u)) + (u + 1) 4 + 2u = -6(2 + 2u + (1u + u2)) + (u + 1) Combine like terms: 2u + 1u = 3u 4 + 2u = -6(2 + 3u + u2) + (u + 1) 4 + 2u = (2 * -6 + 3u * -6 + u2 * -6) + (u + 1) 4 + 2u = (-12 + -18u + -6u2) + (u + 1) Reorder the terms: 4 + 2u = -12 + -18u + -6u2 + (1 + u) Remove parenthesis around (1 + u) 4 + 2u = -12 + -18u + -6u2 + 1 + u Reorder the terms: 4 + 2u = -12 + 1 + -18u + u + -6u2 Combine like terms: -12 + 1 = -11 4 + 2u = -11 + -18u + u + -6u2 Combine like terms: -18u + u = -17u 4 + 2u = -11 + -17u + -6u2 Solving 4 + 2u = -11 + -17u + -6u2 Solving for variable 'u'. Reorder the terms: 4 + 11 + 2u + 17u + 6u2 = -11 + -17u + -6u2 + 11 + 17u + 6u2 Combine like terms: 4 + 11 = 15 15 + 2u + 17u + 6u2 = -11 + -17u + -6u2 + 11 + 17u + 6u2 Combine like terms: 2u + 17u = 19u 15 + 19u + 6u2 = -11 + -17u + -6u2 + 11 + 17u + 6u2 Reorder the terms: 15 + 19u + 6u2 = -11 + 11 + -17u + 17u + -6u2 + 6u2 Combine like terms: -11 + 11 = 0 15 + 19u + 6u2 = 0 + -17u + 17u + -6u2 + 6u2 15 + 19u + 6u2 = -17u + 17u + -6u2 + 6u2 Combine like terms: -17u + 17u = 0 15 + 19u + 6u2 = 0 + -6u2 + 6u2 15 + 19u + 6u2 = -6u2 + 6u2 Combine like terms: -6u2 + 6u2 = 0 15 + 19u + 6u2 = 0 Factor a trinomial. (5 + 3u)(3 + 2u) = 0Subproblem 1
Set the factor '(5 + 3u)' equal to zero and attempt to solve: Simplifying 5 + 3u = 0 Solving 5 + 3u = 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 + 3u = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3u = 0 + -5 3u = 0 + -5 Combine like terms: 0 + -5 = -5 3u = -5 Divide each side by '3'. u = -1.666666667 Simplifying u = -1.666666667Subproblem 2
Set the factor '(3 + 2u)' equal to zero and attempt to solve: Simplifying 3 + 2u = 0 Solving 3 + 2u = 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 + 2u = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2u = 0 + -3 2u = 0 + -3 Combine like terms: 0 + -3 = -3 2u = -3 Divide each side by '2'. u = -1.5 Simplifying u = -1.5Solution
u = {-1.666666667, -1.5}
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