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Simplifying (4u + 2)(7 + u) = 0 Reorder the terms: (2 + 4u)(7 + u) = 0 Multiply (2 + 4u) * (7 + u) (2(7 + u) + 4u * (7 + u)) = 0 ((7 * 2 + u * 2) + 4u * (7 + u)) = 0 ((14 + 2u) + 4u * (7 + u)) = 0 (14 + 2u + (7 * 4u + u * 4u)) = 0 (14 + 2u + (28u + 4u2)) = 0 Combine like terms: 2u + 28u = 30u (14 + 30u + 4u2) = 0 Solving 14 + 30u + 4u2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '2'. 2(7 + 15u + 2u2) = 0 Factor a trinomial. 2((7 + u)(1 + 2u)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + u)' equal to zero and attempt to solve: Simplifying 7 + u = 0 Solving 7 + u = 0 Move all terms containing u to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + u = 0 + -7 Combine like terms: 7 + -7 = 0 0 + u = 0 + -7 u = 0 + -7 Combine like terms: 0 + -7 = -7 u = -7 Simplifying u = -7Subproblem 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 = {-7, -0.5}
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