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Simplifying 7 = -5n2 + -19n + -5 Reorder the terms: 7 = -5 + -19n + -5n2 Solving 7 = -5 + -19n + -5n2 Solving for variable 'n'. Combine like terms: 7 + 5 = 12 12 + 19n + 5n2 = -5 + -19n + -5n2 + 5 + 19n + 5n2 Reorder the terms: 12 + 19n + 5n2 = -5 + 5 + -19n + 19n + -5n2 + 5n2 Combine like terms: -5 + 5 = 0 12 + 19n + 5n2 = 0 + -19n + 19n + -5n2 + 5n2 12 + 19n + 5n2 = -19n + 19n + -5n2 + 5n2 Combine like terms: -19n + 19n = 0 12 + 19n + 5n2 = 0 + -5n2 + 5n2 12 + 19n + 5n2 = -5n2 + 5n2 Combine like terms: -5n2 + 5n2 = 0 12 + 19n + 5n2 = 0 Factor a trinomial. (3 + n)(4 + 5n) = 0Subproblem 1
Set the factor '(3 + n)' equal to zero and attempt to solve: Simplifying 3 + n = 0 Solving 3 + n = 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 + n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + n = 0 + -3 n = 0 + -3 Combine like terms: 0 + -3 = -3 n = -3 Simplifying n = -3Subproblem 2
Set the factor '(4 + 5n)' equal to zero and attempt to solve: Simplifying 4 + 5n = 0 Solving 4 + 5n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 5n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5n = 0 + -4 5n = 0 + -4 Combine like terms: 0 + -4 = -4 5n = -4 Divide each side by '5'. n = -0.8 Simplifying n = -0.8Solution
n = {-3, -0.8}
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