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Simplifying 5n2 = -16 + -18n Solving 5n2 = -16 + -18n Solving for variable 'n'. Reorder the terms: 16 + 18n + 5n2 = -16 + -18n + 16 + 18n Reorder the terms: 16 + 18n + 5n2 = -16 + 16 + -18n + 18n Combine like terms: -16 + 16 = 0 16 + 18n + 5n2 = 0 + -18n + 18n 16 + 18n + 5n2 = -18n + 18n Combine like terms: -18n + 18n = 0 16 + 18n + 5n2 = 0 Factor a trinomial. (2 + n)(8 + 5n) = 0Subproblem 1
Set the factor '(2 + n)' equal to zero and attempt to solve: Simplifying 2 + n = 0 Solving 2 + n = 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 + n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + n = 0 + -2 n = 0 + -2 Combine like terms: 0 + -2 = -2 n = -2 Simplifying n = -2Subproblem 2
Set the factor '(8 + 5n)' equal to zero and attempt to solve: Simplifying 8 + 5n = 0 Solving 8 + 5n = 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 + 5n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 5n = 0 + -8 5n = 0 + -8 Combine like terms: 0 + -8 = -8 5n = -8 Divide each side by '5'. n = -1.6 Simplifying n = -1.6Solution
n = {-2, -1.6}
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