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Simplifying 2n2 = -24 + -19n Solving 2n2 = -24 + -19n Solving for variable 'n'. Reorder the terms: 24 + 19n + 2n2 = -24 + -19n + 24 + 19n Reorder the terms: 24 + 19n + 2n2 = -24 + 24 + -19n + 19n Combine like terms: -24 + 24 = 0 24 + 19n + 2n2 = 0 + -19n + 19n 24 + 19n + 2n2 = -19n + 19n Combine like terms: -19n + 19n = 0 24 + 19n + 2n2 = 0 Factor a trinomial. (8 + n)(3 + 2n) = 0Subproblem 1
Set the factor '(8 + n)' equal to zero and attempt to solve: Simplifying 8 + n = 0 Solving 8 + n = 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 + n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + n = 0 + -8 n = 0 + -8 Combine like terms: 0 + -8 = -8 n = -8 Simplifying n = -8Subproblem 2
Set the factor '(3 + 2n)' equal to zero and attempt to solve: Simplifying 3 + 2n = 0 Solving 3 + 2n = 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 + 2n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2n = 0 + -3 2n = 0 + -3 Combine like terms: 0 + -3 = -3 2n = -3 Divide each side by '2'. n = -1.5 Simplifying n = -1.5Solution
n = {-8, -1.5}
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