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Simplifying 5n2 + 41n + 40 = -2 Reorder the terms: 40 + 41n + 5n2 = -2 Solving 40 + 41n + 5n2 = -2 Solving for variable 'n'. Reorder the terms: 40 + 2 + 41n + 5n2 = -2 + 2 Combine like terms: 40 + 2 = 42 42 + 41n + 5n2 = -2 + 2 Combine like terms: -2 + 2 = 0 42 + 41n + 5n2 = 0 Factor a trinomial. (7 + n)(6 + 5n) = 0Subproblem 1
Set the factor '(7 + n)' equal to zero and attempt to solve: Simplifying 7 + n = 0 Solving 7 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + n = 0 + -7 n = 0 + -7 Combine like terms: 0 + -7 = -7 n = -7 Simplifying n = -7Subproblem 2
Set the factor '(6 + 5n)' equal to zero and attempt to solve: Simplifying 6 + 5n = 0 Solving 6 + 5n = 0 Move all terms containing n to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + 5n = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 5n = 0 + -6 5n = 0 + -6 Combine like terms: 0 + -6 = -6 5n = -6 Divide each side by '5'. n = -1.2 Simplifying n = -1.2Solution
n = {-7, -1.2}
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