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Simplifying 3n2 + n = 24 Reorder the terms: n + 3n2 = 24 Solving n + 3n2 = 24 Solving for variable 'n'. Reorder the terms: -24 + n + 3n2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + n + 3n2 = 0 Factor a trinomial. (-3 + -1n)(8 + -3n) = 0Subproblem 1
Set the factor '(-3 + -1n)' equal to zero and attempt to solve: Simplifying -3 + -1n = 0 Solving -3 + -1n = 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 + -1n = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1n = 0 + 3 -1n = 0 + 3 Combine like terms: 0 + 3 = 3 -1n = 3 Divide each side by '-1'. 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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