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Simplifying (n + -3)(n + -7) = 0 Reorder the terms: (-3 + n)(n + -7) = 0 Reorder the terms: (-3 + n)(-7 + n) = 0 Multiply (-3 + n) * (-7 + n) (-3(-7 + n) + n(-7 + n)) = 0 ((-7 * -3 + n * -3) + n(-7 + n)) = 0 ((21 + -3n) + n(-7 + n)) = 0 (21 + -3n + (-7 * n + n * n)) = 0 (21 + -3n + (-7n + n2)) = 0 Combine like terms: -3n + -7n = -10n (21 + -10n + n2) = 0 Solving 21 + -10n + n2 = 0 Solving for variable 'n'. Factor a trinomial. (3 + -1n)(7 + -1n) = 0Subproblem 1
Set the factor '(3 + -1n)' equal to zero and attempt to solve: Simplifying 3 + -1n = 0 Solving 3 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1n = 0 + -3 -1n = 0 + -3 Combine like terms: 0 + -3 = -3 -1n = -3 Divide each side by '-1'. n = 3 Simplifying n = 3Subproblem 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 = {3, 7}
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