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Simplifying (4u + -6)(8 + u) = 0 Reorder the terms: (-6 + 4u)(8 + u) = 0 Multiply (-6 + 4u) * (8 + u) (-6(8 + u) + 4u * (8 + u)) = 0 ((8 * -6 + u * -6) + 4u * (8 + u)) = 0 ((-48 + -6u) + 4u * (8 + u)) = 0 (-48 + -6u + (8 * 4u + u * 4u)) = 0 (-48 + -6u + (32u + 4u2)) = 0 Combine like terms: -6u + 32u = 26u (-48 + 26u + 4u2) = 0 Solving -48 + 26u + 4u2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '2'. 2(-24 + 13u + 2u2) = 0 Factor a trinomial. 2((-8 + -1u)(3 + -2u)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + -1u)' equal to zero and attempt to solve: Simplifying -8 + -1u = 0 Solving -8 + -1u = 0 Move all terms containing u to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1u = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1u = 0 + 8 -1u = 0 + 8 Combine like terms: 0 + 8 = 8 -1u = 8 Divide each side by '-1'. u = -8 Simplifying u = -8Subproblem 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 = {-8, 1.5}
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