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Simplifying (n + 1)(n + -7) = 0 Reorder the terms: (1 + n)(n + -7) = 0 Reorder the terms: (1 + n)(-7 + n) = 0 Multiply (1 + n) * (-7 + n) (1(-7 + n) + n(-7 + n)) = 0 ((-7 * 1 + n * 1) + n(-7 + n)) = 0 ((-7 + 1n) + n(-7 + n)) = 0 (-7 + 1n + (-7 * n + n * n)) = 0 (-7 + 1n + (-7n + n2)) = 0 Combine like terms: 1n + -7n = -6n (-7 + -6n + n2) = 0 Solving -7 + -6n + n2 = 0 Solving for variable 'n'. Factor a trinomial. (-1 + -1n)(7 + -1n) = 0Subproblem 1
Set the factor '(-1 + -1n)' equal to zero and attempt to solve: Simplifying -1 + -1n = 0 Solving -1 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1n = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1n = 0 + 1 -1n = 0 + 1 Combine like terms: 0 + 1 = 1 -1n = 1 Divide each side by '-1'. n = -1 Simplifying n = -1Subproblem 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 = {-1, 7}
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