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Simplifying (3n + 1)(3n + 1) = 0 Reorder the terms: (1 + 3n)(3n + 1) = 0 Reorder the terms: (1 + 3n)(1 + 3n) = 0 Multiply (1 + 3n) * (1 + 3n) (1(1 + 3n) + 3n * (1 + 3n)) = 0 ((1 * 1 + 3n * 1) + 3n * (1 + 3n)) = 0 ((1 + 3n) + 3n * (1 + 3n)) = 0 (1 + 3n + (1 * 3n + 3n * 3n)) = 0 (1 + 3n + (3n + 9n2)) = 0 Combine like terms: 3n + 3n = 6n (1 + 6n + 9n2) = 0 Solving 1 + 6n + 9n2 = 0 Solving for variable 'n'. Factor a trinomial. (1 + 3n)(1 + 3n) = 0Subproblem 1
Set the factor '(1 + 3n)' equal to zero and attempt to solve: Simplifying 1 + 3n = 0 Solving 1 + 3n = 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 + 3n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3n = 0 + -1 3n = 0 + -1 Combine like terms: 0 + -1 = -1 3n = -1 Divide each side by '3'. n = -0.3333333333 Simplifying n = -0.3333333333Subproblem 2
Set the factor '(1 + 3n)' equal to zero and attempt to solve: Simplifying 1 + 3n = 0 Solving 1 + 3n = 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 + 3n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3n = 0 + -1 3n = 0 + -1 Combine like terms: 0 + -1 = -1 3n = -1 Divide each side by '3'. n = -0.3333333333 Simplifying n = -0.3333333333Solution
n = {-0.3333333333, -0.3333333333}
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