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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 = 22u (-42 + 22u + 4u2) = 0 Solving -42 + 22u + 4u2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '2'. 2(-21 + 11u + 2u2) = 0 Factor a trinomial. 2((-7 + -1u)(3 + -2u)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + -1u)' equal to zero and attempt to solve: Simplifying -7 + -1u = 0 Solving -7 + -1u = 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 + -1u = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1u = 0 + 7 -1u = 0 + 7 Combine like terms: 0 + 7 = 7 -1u = 7 Divide each side by '-1'. 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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