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Simplifying (n + -13)(n + -27) = 0 Reorder the terms: (-13 + n)(n + -27) = 0 Reorder the terms: (-13 + n)(-27 + n) = 0 Multiply (-13 + n) * (-27 + n) (-13(-27 + n) + n(-27 + n)) = 0 ((-27 * -13 + n * -13) + n(-27 + n)) = 0 ((351 + -13n) + n(-27 + n)) = 0 (351 + -13n + (-27 * n + n * n)) = 0 (351 + -13n + (-27n + n2)) = 0 Combine like terms: -13n + -27n = -40n (351 + -40n + n2) = 0 Solving 351 + -40n + n2 = 0 Solving for variable 'n'. Factor a trinomial. (13 + -1n)(27 + -1n) = 0Subproblem 1
Set the factor '(13 + -1n)' equal to zero and attempt to solve: Simplifying 13 + -1n = 0 Solving 13 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -1n = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -1n = 0 + -13 -1n = 0 + -13 Combine like terms: 0 + -13 = -13 -1n = -13 Divide each side by '-1'. n = 13 Simplifying n = 13Subproblem 2
Set the factor '(27 + -1n)' equal to zero and attempt to solve: Simplifying 27 + -1n = 0 Solving 27 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -27 + -1n = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -1n = 0 + -27 -1n = 0 + -27 Combine like terms: 0 + -27 = -27 -1n = -27 Divide each side by '-1'. n = 27 Simplifying n = 27Solution
n = {13, 27}
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