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Simplifying (4 + u)(4u + -2) = 0 Reorder the terms: (4 + u)(-2 + 4u) = 0 Multiply (4 + u) * (-2 + 4u) (4(-2 + 4u) + u(-2 + 4u)) = 0 ((-2 * 4 + 4u * 4) + u(-2 + 4u)) = 0 ((-8 + 16u) + u(-2 + 4u)) = 0 (-8 + 16u + (-2 * u + 4u * u)) = 0 (-8 + 16u + (-2u + 4u2)) = 0 Combine like terms: 16u + -2u = 14u (-8 + 14u + 4u2) = 0 Solving -8 + 14u + 4u2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 7u + 2u2) = 0 Factor a trinomial. 2((-4 + -1u)(1 + -2u)) = 0 Ignore the factor 2.Subproblem 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 + -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 = {-4, 0.5}
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