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Simplifying 7n2 + 11 = -7 + -27n Reorder the terms: 11 + 7n2 = -7 + -27n Solving 11 + 7n2 = -7 + -27n Solving for variable 'n'. Reorder the terms: 11 + 7 + 27n + 7n2 = -7 + -27n + 7 + 27n Combine like terms: 11 + 7 = 18 18 + 27n + 7n2 = -7 + -27n + 7 + 27n Reorder the terms: 18 + 27n + 7n2 = -7 + 7 + -27n + 27n Combine like terms: -7 + 7 = 0 18 + 27n + 7n2 = 0 + -27n + 27n 18 + 27n + 7n2 = -27n + 27n Combine like terms: -27n + 27n = 0 18 + 27n + 7n2 = 0 Factor a trinomial. (3 + n)(6 + 7n) = 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 '(6 + 7n)' equal to zero and attempt to solve: Simplifying 6 + 7n = 0 Solving 6 + 7n = 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 + 7n = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 7n = 0 + -6 7n = 0 + -6 Combine like terms: 0 + -6 = -6 7n = -6 Divide each side by '7'. n = -0.8571428571 Simplifying n = -0.8571428571Solution
n = {-3, -0.8571428571}
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