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Simplifying (8 + u)(2u + -1) = 0 Reorder the terms: (8 + u)(-1 + 2u) = 0 Multiply (8 + u) * (-1 + 2u) (8(-1 + 2u) + u(-1 + 2u)) = 0 ((-1 * 8 + 2u * 8) + u(-1 + 2u)) = 0 ((-8 + 16u) + u(-1 + 2u)) = 0 (-8 + 16u + (-1 * u + 2u * u)) = 0 (-8 + 16u + (-1u + 2u2)) = 0 Combine like terms: 16u + -1u = 15u (-8 + 15u + 2u2) = 0 Solving -8 + 15u + 2u2 = 0 Solving for variable 'u'. Factor a trinomial. (-8 + -1u)(1 + -2u) = 0Subproblem 1
Set the factor '(-8 + -1u)' equal to zero and attempt to solve: Simplifying -8 + -1u = 0 Solving -8 + -1u = 0 Move all terms containing u to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1u = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1u = 0 + 8 -1u = 0 + 8 Combine like terms: 0 + 8 = 8 -1u = 8 Divide each side by '-1'. u = -8 Simplifying u = -8Subproblem 2
Set the factor '(1 + -2u)' equal to zero and attempt to solve: Simplifying 1 + -2u = 0 Solving 1 + -2u = 0 Move all terms containing u to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2u = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2u = 0 + -1 -2u = 0 + -1 Combine like terms: 0 + -1 = -1 -2u = -1 Divide each side by '-2'. u = 0.5 Simplifying u = 0.5Solution
u = {-8, 0.5}
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