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Simplifying (3n + 7)(n + -9) = 0 Reorder the terms: (7 + 3n)(n + -9) = 0 Reorder the terms: (7 + 3n)(-9 + n) = 0 Multiply (7 + 3n) * (-9 + n) (7(-9 + n) + 3n * (-9 + n)) = 0 ((-9 * 7 + n * 7) + 3n * (-9 + n)) = 0 ((-63 + 7n) + 3n * (-9 + n)) = 0 (-63 + 7n + (-9 * 3n + n * 3n)) = 0 (-63 + 7n + (-27n + 3n2)) = 0 Combine like terms: 7n + -27n = -20n (-63 + -20n + 3n2) = 0 Solving -63 + -20n + 3n2 = 0 Solving for variable 'n'. Factor a trinomial. (-7 + -3n)(9 + -1n) = 0Subproblem 1
Set the factor '(-7 + -3n)' equal to zero and attempt to solve: Simplifying -7 + -3n = 0 Solving -7 + -3n = 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 + -3n = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -3n = 0 + 7 -3n = 0 + 7 Combine like terms: 0 + 7 = 7 -3n = 7 Divide each side by '-3'. n = -2.333333333 Simplifying n = -2.333333333Subproblem 2
Set the factor '(9 + -1n)' equal to zero and attempt to solve: Simplifying 9 + -1n = 0 Solving 9 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1n = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1n = 0 + -9 -1n = 0 + -9 Combine like terms: 0 + -9 = -9 -1n = -9 Divide each side by '-1'. n = 9 Simplifying n = 9Solution
n = {-2.333333333, 9}
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