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Simplifying 27n2 + 6n + -16 = 0 Reorder the terms: -16 + 6n + 27n2 = 0 Solving -16 + 6n + 27n2 = 0 Solving for variable 'n'. Factor a trinomial. (-8 + -9n)(2 + -3n) = 0Subproblem 1
Set the factor '(-8 + -9n)' equal to zero and attempt to solve: Simplifying -8 + -9n = 0 Solving -8 + -9n = 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 + -9n = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -9n = 0 + 8 -9n = 0 + 8 Combine like terms: 0 + 8 = 8 -9n = 8 Divide each side by '-9'. n = -0.8888888889 Simplifying n = -0.8888888889Subproblem 2
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 = 0.6666666667Solution
n = {-0.8888888889, 0.6666666667}
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