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Simplifying (4 + -1u)(4u + 1) = 0 Reorder the terms: (4 + -1u)(1 + 4u) = 0 Multiply (4 + -1u) * (1 + 4u) (4(1 + 4u) + -1u * (1 + 4u)) = 0 ((1 * 4 + 4u * 4) + -1u * (1 + 4u)) = 0 ((4 + 16u) + -1u * (1 + 4u)) = 0 (4 + 16u + (1 * -1u + 4u * -1u)) = 0 (4 + 16u + (-1u + -4u2)) = 0 Combine like terms: 16u + -1u = 15u (4 + 15u + -4u2) = 0 Solving 4 + 15u + -4u2 = 0 Solving for variable 'u'. Factor a trinomial. (4 + -1u)(1 + 4u) = 0Subproblem 1
Set the factor '(4 + -1u)' equal to zero and attempt to solve: Simplifying 4 + -1u = 0 Solving 4 + -1u = 0 Move all terms containing u to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1u = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1u = 0 + -4 -1u = 0 + -4 Combine like terms: 0 + -4 = -4 -1u = -4 Divide each side by '-1'. u = 4 Simplifying u = 4Subproblem 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 = {4, -0.25}
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