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Simplifying (8 + -1u)(4u + -2) = 0 Reorder the terms: (8 + -1u)(-2 + 4u) = 0 Multiply (8 + -1u) * (-2 + 4u) (8(-2 + 4u) + -1u * (-2 + 4u)) = 0 ((-2 * 8 + 4u * 8) + -1u * (-2 + 4u)) = 0 ((-16 + 32u) + -1u * (-2 + 4u)) = 0 (-16 + 32u + (-2 * -1u + 4u * -1u)) = 0 (-16 + 32u + (2u + -4u2)) = 0 Combine like terms: 32u + 2u = 34u (-16 + 34u + -4u2) = 0 Solving -16 + 34u + -4u2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + 17u + -2u2) = 0 Factor a trinomial. 2((-8 + u)(1 + -2u)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + u)' equal to zero and attempt to solve: Simplifying -8 + u = 0 Solving -8 + u = 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 + u = 0 + 8 Combine like terms: -8 + 8 = 0 0 + u = 0 + 8 u = 0 + 8 Combine like terms: 0 + 8 = 8 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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