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Simplifying (4u + 6)(7 + u) = 0 Reorder the terms: (6 + 4u)(7 + u) = 0 Multiply (6 + 4u) * (7 + u) (6(7 + u) + 4u * (7 + u)) = 0 ((7 * 6 + u * 6) + 4u * (7 + u)) = 0 ((42 + 6u) + 4u * (7 + u)) = 0 (42 + 6u + (7 * 4u + u * 4u)) = 0 (42 + 6u + (28u + 4u2)) = 0 Combine like terms: 6u + 28u = 34u (42 + 34u + 4u2) = 0 Solving 42 + 34u + 4u2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '2'. 2(21 + 17u + 2u2) = 0 Factor a trinomial. 2((7 + u)(3 + 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 '(3 + 2u)' equal to zero and attempt to solve: Simplifying 3 + 2u = 0 Solving 3 + 2u = 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 + 2u = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2u = 0 + -3 2u = 0 + -3 Combine like terms: 0 + -3 = -3 2u = -3 Divide each side by '2'. u = -1.5 Simplifying u = -1.5Solution
u = {-7, -1.5}
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