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Simplifying (4 + -2u)(3 + u) = 0 Multiply (4 + -2u) * (3 + u) (4(3 + u) + -2u * (3 + u)) = 0 ((3 * 4 + u * 4) + -2u * (3 + u)) = 0 ((12 + 4u) + -2u * (3 + u)) = 0 (12 + 4u + (3 * -2u + u * -2u)) = 0 (12 + 4u + (-6u + -2u2)) = 0 Combine like terms: 4u + -6u = -2u (12 + -2u + -2u2) = 0 Solving 12 + -2u + -2u2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '2'. 2(6 + -1u + -1u2) = 0 Factor a trinomial. 2((2 + -1u)(3 + u)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -1u)' equal to zero and attempt to solve: Simplifying 2 + -1u = 0 Solving 2 + -1u = 0 Move all terms containing u to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1u = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1u = 0 + -2 -1u = 0 + -2 Combine like terms: 0 + -2 = -2 -1u = -2 Divide each side by '-1'. u = 2 Simplifying u = 2Subproblem 2
Set the factor '(3 + u)' equal to zero and attempt to solve: Simplifying 3 + u = 0 Solving 3 + u = 0 Move all terms containing u to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + u = 0 + -3 Combine like terms: 3 + -3 = 0 0 + u = 0 + -3 u = 0 + -3 Combine like terms: 0 + -3 = -3 u = -3 Simplifying u = -3Solution
u = {2, -3}
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