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Simplifying 14n2 + -18n + -16 = 5n2 Reorder the terms: -16 + -18n + 14n2 = 5n2 Solving -16 + -18n + 14n2 = 5n2 Solving for variable 'n'. Combine like terms: 14n2 + -5n2 = 9n2 -16 + -18n + 9n2 = 5n2 + -5n2 Combine like terms: 5n2 + -5n2 = 0 -16 + -18n + 9n2 = 0 Factor a trinomial. (-2 + -3n)(8 + -3n) = 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 '(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 = {-0.6666666667, 2.666666667}
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