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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. (-5 + -1u)(7 + -1u) = 0Subproblem 1
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 = -5Subproblem 2
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 = 7Solution
u = {-5, 7}
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