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Simplifying (4u + -1)(8 + u) = 0 Reorder the terms: (-1 + 4u)(8 + u) = 0 Multiply (-1 + 4u) * (8 + u) (-1(8 + u) + 4u * (8 + u)) = 0 ((8 * -1 + u * -1) + 4u * (8 + u)) = 0 ((-8 + -1u) + 4u * (8 + u)) = 0 (-8 + -1u + (8 * 4u + u * 4u)) = 0 (-8 + -1u + (32u + 4u2)) = 0 Combine like terms: -1u + 32u = 31u (-8 + 31u + 4u2) = 0 Solving -8 + 31u + 4u2 = 0 Solving for variable 'u'. Factor a trinomial. (-8 + -1u)(1 + -4u) = 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 + -4u)' equal to zero and attempt to solve: Simplifying 1 + -4u = 0 Solving 1 + -4u = 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 + -4u = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4u = 0 + -1 -4u = 0 + -1 Combine like terms: 0 + -1 = -1 -4u = -1 Divide each side by '-4'. u = 0.25 Simplifying u = 0.25Solution
u = {-8, 0.25}
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