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Simplifying (n + -4)(n + -7) = 0 Reorder the terms: (-4 + n)(n + -7) = 0 Reorder the terms: (-4 + n)(-7 + n) = 0 Multiply (-4 + n) * (-7 + n) (-4(-7 + n) + n(-7 + n)) = 0 ((-7 * -4 + n * -4) + n(-7 + n)) = 0 ((28 + -4n) + n(-7 + n)) = 0 (28 + -4n + (-7 * n + n * n)) = 0 (28 + -4n + (-7n + n2)) = 0 Combine like terms: -4n + -7n = -11n (28 + -11n + n2) = 0 Solving 28 + -11n + n2 = 0 Solving for variable 'n'. Factor a trinomial. (4 + -1n)(7 + -1n) = 0Subproblem 1
Set the factor '(4 + -1n)' equal to zero and attempt to solve: Simplifying 4 + -1n = 0 Solving 4 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1n = 0 + -4 -1n = 0 + -4 Combine like terms: 0 + -4 = -4 -1n = -4 Divide each side by '-1'. n = 4 Simplifying n = 4Subproblem 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 = {4, 7}
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