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Simplifying (n + -6)(n + 1) = 0 Reorder the terms: (-6 + n)(n + 1) = 0 Reorder the terms: (-6 + n)(1 + n) = 0 Multiply (-6 + n) * (1 + n) (-6(1 + n) + n(1 + n)) = 0 ((1 * -6 + n * -6) + n(1 + n)) = 0 ((-6 + -6n) + n(1 + n)) = 0 (-6 + -6n + (1 * n + n * n)) = 0 (-6 + -6n + (1n + n2)) = 0 Combine like terms: -6n + 1n = -5n (-6 + -5n + n2) = 0 Solving -6 + -5n + n2 = 0 Solving for variable 'n'. Factor a trinomial. (-1 + -1n)(6 + -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 '(6 + -1n)' equal to zero and attempt to solve: Simplifying 6 + -1n = 0 Solving 6 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1n = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1n = 0 + -6 -1n = 0 + -6 Combine like terms: 0 + -6 = -6 -1n = -6 Divide each side by '-1'. n = 6 Simplifying n = 6Solution
n = {-1, 6}
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