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Simplifying 3n2 + -23n + 20 = 6 Reorder the terms: 20 + -23n + 3n2 = 6 Solving 20 + -23n + 3n2 = 6 Solving for variable 'n'. Reorder the terms: 20 + -6 + -23n + 3n2 = 6 + -6 Combine like terms: 20 + -6 = 14 14 + -23n + 3n2 = 6 + -6 Combine like terms: 6 + -6 = 0 14 + -23n + 3n2 = 0 Factor a trinomial. (2 + -3n)(7 + -1n) = 0Subproblem 1
Set the factor '(2 + -3n)' equal to zero and attempt to solve: Simplifying 2 + -3n = 0 Solving 2 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3n = 0 + -2 -3n = 0 + -2 Combine like terms: 0 + -2 = -2 -3n = -2 Divide each side by '-3'. n = 0.6666666667 Simplifying n = 0.6666666667Subproblem 2
Set the factor '(7 + -1n)' equal to zero and attempt to solve: Simplifying 7 + -1n = 0 Solving 7 + -1n = 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 + -1n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1n = 0 + -7 -1n = 0 + -7 Combine like terms: 0 + -7 = -7 -1n = -7 Divide each side by '-1'. n = 7 Simplifying n = 7Solution
n = {0.6666666667, 7}
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