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Simplifying 75(u + -9)(2u + -5) = 0 Reorder the terms: 75(-9 + u)(2u + -5) = 0 Reorder the terms: 75(-9 + u)(-5 + 2u) = 0 Multiply (-9 + u) * (-5 + 2u) 75(-9(-5 + 2u) + u(-5 + 2u)) = 0 75((-5 * -9 + 2u * -9) + u(-5 + 2u)) = 0 75((45 + -18u) + u(-5 + 2u)) = 0 75(45 + -18u + (-5 * u + 2u * u)) = 0 75(45 + -18u + (-5u + 2u2)) = 0 Combine like terms: -18u + -5u = -23u 75(45 + -23u + 2u2) = 0 (45 * 75 + -23u * 75 + 2u2 * 75) = 0 (3375 + -1725u + 150u2) = 0 Solving 3375 + -1725u + 150u2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '75'. 75(45 + -23u + 2u2) = 0 Factor a trinomial. 75((5 + -2u)(9 + -1u)) = 0 Ignore the factor 75.Subproblem 1
Set the factor '(5 + -2u)' equal to zero and attempt to solve: Simplifying 5 + -2u = 0 Solving 5 + -2u = 0 Move all terms containing u to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2u = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2u = 0 + -5 -2u = 0 + -5 Combine like terms: 0 + -5 = -5 -2u = -5 Divide each side by '-2'. u = 2.5 Simplifying u = 2.5Subproblem 2
Set the factor '(9 + -1u)' equal to zero and attempt to solve: Simplifying 9 + -1u = 0 Solving 9 + -1u = 0 Move all terms containing u to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1u = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1u = 0 + -9 -1u = 0 + -9 Combine like terms: 0 + -9 = -9 -1u = -9 Divide each side by '-1'. u = 9 Simplifying u = 9Solution
u = {2.5, 9}
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