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Simplifying 6n2 + -41n + 11 = 18 Reorder the terms: 11 + -41n + 6n2 = 18 Solving 11 + -41n + 6n2 = 18 Solving for variable 'n'. Reorder the terms: 11 + -18 + -41n + 6n2 = 18 + -18 Combine like terms: 11 + -18 = -7 -7 + -41n + 6n2 = 18 + -18 Combine like terms: 18 + -18 = 0 -7 + -41n + 6n2 = 0 Factor a trinomial. (-1 + -6n)(7 + -1n) = 0Subproblem 1
Set the factor '(-1 + -6n)' equal to zero and attempt to solve: Simplifying -1 + -6n = 0 Solving -1 + -6n = 0 Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -6n = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -6n = 0 + 1 -6n = 0 + 1 Combine like terms: 0 + 1 = 1 -6n = 1 Divide each side by '-6'. n = -0.1666666667 Simplifying n = -0.1666666667Subproblem 2
Set the factor '(7 + -1n)' equal to zero and attempt to solve: Simplifying 7 + -1n = 0 Solving 7 + -1n = 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 + -1n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1n = 0 + -7 -1n = 0 + -7 Combine like terms: 0 + -7 = -7 -1n = -7 Divide each side by '-1'. n = 7 Simplifying n = 7Solution
n = {-0.1666666667, 7}
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