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Simplifying -5n2 + 7n + 13 = -11 Reorder the terms: 13 + 7n + -5n2 = -11 Solving 13 + 7n + -5n2 = -11 Solving for variable 'n'. Reorder the terms: 13 + 11 + 7n + -5n2 = -11 + 11 Combine like terms: 13 + 11 = 24 24 + 7n + -5n2 = -11 + 11 Combine like terms: -11 + 11 = 0 24 + 7n + -5n2 = 0 Factor a trinomial. (3 + -1n)(8 + 5n) = 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 + 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 = {3, -1.6}
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