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Simplifying 6n2 + 9n + 5 = 11 Reorder the terms: 5 + 9n + 6n2 = 11 Solving 5 + 9n + 6n2 = 11 Solving for variable 'n'. Reorder the terms: 5 + -11 + 9n + 6n2 = 11 + -11 Combine like terms: 5 + -11 = -6 -6 + 9n + 6n2 = 11 + -11 Combine like terms: 11 + -11 = 0 -6 + 9n + 6n2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-2 + 3n + 2n2) = 0 Factor a trinomial. 3((-2 + -1n)(1 + -2n)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2 + -1n)' equal to zero and attempt to solve: Simplifying -2 + -1n = 0 Solving -2 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1n = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1n = 0 + 2 -1n = 0 + 2 Combine like terms: 0 + 2 = 2 -1n = 2 Divide each side by '-1'. n = -2 Simplifying n = -2Subproblem 2
Set the factor '(1 + -2n)' equal to zero and attempt to solve: Simplifying 1 + -2n = 0 Solving 1 + -2n = 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 + -2n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2n = 0 + -1 -2n = 0 + -1 Combine like terms: 0 + -1 = -1 -2n = -1 Divide each side by '-2'. n = 0.5 Simplifying n = 0.5Solution
n = {-2, 0.5}
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