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Simplifying (n + -7)(n + 24) = 0 Reorder the terms: (-7 + n)(n + 24) = 0 Reorder the terms: (-7 + n)(24 + n) = 0 Multiply (-7 + n) * (24 + n) (-7(24 + n) + n(24 + n)) = 0 ((24 * -7 + n * -7) + n(24 + n)) = 0 ((-168 + -7n) + n(24 + n)) = 0 (-168 + -7n + (24 * n + n * n)) = 0 (-168 + -7n + (24n + n2)) = 0 Combine like terms: -7n + 24n = 17n (-168 + 17n + n2) = 0 Solving -168 + 17n + n2 = 0 Solving for variable 'n'. Factor a trinomial. (-24 + -1n)(7 + -1n) = 0Subproblem 1
Set the factor '(-24 + -1n)' equal to zero and attempt to solve: Simplifying -24 + -1n = 0 Solving -24 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + -1n = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -1n = 0 + 24 -1n = 0 + 24 Combine like terms: 0 + 24 = 24 -1n = 24 Divide each side by '-1'. n = -24 Simplifying n = -24Subproblem 2
Set the factor '(7 + -1n)' equal to zero and attempt to solve: Simplifying 7 + -1n = 0 Solving 7 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1n = 0 + -7 -1n = 0 + -7 Combine like terms: 0 + -7 = -7 -1n = -7 Divide each side by '-1'. n = 7 Simplifying n = 7Solution
n = {-24, 7}
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