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Simplifying 3n2 = -24 + -17n Solving 3n2 = -24 + -17n Solving for variable 'n'. Reorder the terms: 24 + 17n + 3n2 = -24 + -17n + 24 + 17n Reorder the terms: 24 + 17n + 3n2 = -24 + 24 + -17n + 17n Combine like terms: -24 + 24 = 0 24 + 17n + 3n2 = 0 + -17n + 17n 24 + 17n + 3n2 = -17n + 17n Combine like terms: -17n + 17n = 0 24 + 17n + 3n2 = 0 Factor a trinomial. (3 + n)(8 + 3n) = 0Subproblem 1
Set the factor '(3 + n)' equal to zero and attempt to solve: Simplifying 3 + n = 0 Solving 3 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + n = 0 + -3 n = 0 + -3 Combine like terms: 0 + -3 = -3 n = -3 Simplifying n = -3Subproblem 2
Set the factor '(8 + 3n)' equal to zero and attempt to solve: Simplifying 8 + 3n = 0 Solving 8 + 3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 3n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 3n = 0 + -8 3n = 0 + -8 Combine like terms: 0 + -8 = -8 3n = -8 Divide each side by '3'. n = -2.666666667 Simplifying n = -2.666666667Solution
n = {-3, -2.666666667}
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