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Simplifying 2u2 = u + 6 Reorder the terms: 2u2 = 6 + u Solving 2u2 = 6 + u Solving for variable 'u'. Reorder the terms: -6 + -1u + 2u2 = 6 + u + -6 + -1u Reorder the terms: -6 + -1u + 2u2 = 6 + -6 + u + -1u Combine like terms: 6 + -6 = 0 -6 + -1u + 2u2 = 0 + u + -1u -6 + -1u + 2u2 = u + -1u Combine like terms: u + -1u = 0 -6 + -1u + 2u2 = 0 Factor a trinomial. (-3 + -2u)(2 + -1u) = 0Subproblem 1
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 = -1.5Subproblem 2
Set the factor '(2 + -1u)' equal to zero and attempt to solve: Simplifying 2 + -1u = 0 Solving 2 + -1u = 0 Move all terms containing u to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1u = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1u = 0 + -2 -1u = 0 + -2 Combine like terms: 0 + -2 = -2 -1u = -2 Divide each side by '-1'. u = 2 Simplifying u = 2Solution
u = {-1.5, 2}
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