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Simplifying (3 + -1u)(4u + 2) = 0 Reorder the terms: (3 + -1u)(2 + 4u) = 0 Multiply (3 + -1u) * (2 + 4u) (3(2 + 4u) + -1u * (2 + 4u)) = 0 ((2 * 3 + 4u * 3) + -1u * (2 + 4u)) = 0 ((6 + 12u) + -1u * (2 + 4u)) = 0 (6 + 12u + (2 * -1u + 4u * -1u)) = 0 (6 + 12u + (-2u + -4u2)) = 0 Combine like terms: 12u + -2u = 10u (6 + 10u + -4u2) = 0 Solving 6 + 10u + -4u2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 5u + -2u2) = 0 Factor a trinomial. 2((3 + -1u)(1 + 2u)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -1u)' equal to zero and attempt to solve: Simplifying 3 + -1u = 0 Solving 3 + -1u = 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 + -1u = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1u = 0 + -3 -1u = 0 + -3 Combine like terms: 0 + -3 = -3 -1u = -3 Divide each side by '-1'. u = 3 Simplifying u = 3Subproblem 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 = {3, -0.5}
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