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Simplifying (-1n + 6)(-3n + -23) = 0 Reorder the terms: (6 + -1n)(-3n + -23) = 0 Reorder the terms: (6 + -1n)(-23 + -3n) = 0 Multiply (6 + -1n) * (-23 + -3n) (6(-23 + -3n) + -1n * (-23 + -3n)) = 0 ((-23 * 6 + -3n * 6) + -1n * (-23 + -3n)) = 0 ((-138 + -18n) + -1n * (-23 + -3n)) = 0 (-138 + -18n + (-23 * -1n + -3n * -1n)) = 0 (-138 + -18n + (23n + 3n2)) = 0 Combine like terms: -18n + 23n = 5n (-138 + 5n + 3n2) = 0 Solving -138 + 5n + 3n2 = 0 Solving for variable 'n'. Factor a trinomial. (-23 + -3n)(6 + -1n) = 0Subproblem 1
Set the factor '(-23 + -3n)' equal to zero and attempt to solve: Simplifying -23 + -3n = 0 Solving -23 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + -3n = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -3n = 0 + 23 -3n = 0 + 23 Combine like terms: 0 + 23 = 23 -3n = 23 Divide each side by '-3'. n = -7.666666667 Simplifying n = -7.666666667Subproblem 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 = {-7.666666667, 6}
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