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Simplifying (u + -5)(u + 7) = 0 Reorder the terms: (-5 + u)(u + 7) = 0 Reorder the terms: (-5 + u)(7 + u) = 0 Multiply (-5 + u) * (7 + u) (-5(7 + u) + u(7 + u)) = 0 ((7 * -5 + u * -5) + u(7 + u)) = 0 ((-35 + -5u) + u(7 + u)) = 0 (-35 + -5u + (7 * u + u * u)) = 0 (-35 + -5u + (7u + u2)) = 0 Combine like terms: -5u + 7u = 2u (-35 + 2u + u2) = 0 Solving -35 + 2u + u2 = 0 Solving for variable 'u'. Factor a trinomial. (-7 + -1u)(5 + -1u) = 0Subproblem 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 '(5 + -1u)' equal to zero and attempt to solve: Simplifying 5 + -1u = 0 Solving 5 + -1u = 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 + -1u = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1u = 0 + -5 -1u = 0 + -5 Combine like terms: 0 + -5 = -5 -1u = -5 Divide each side by '-1'. u = 5 Simplifying u = 5Solution
u = {-7, 5}
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