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Simplifying (3n + -1)(2n + 5) = 0 Reorder the terms: (-1 + 3n)(2n + 5) = 0 Reorder the terms: (-1 + 3n)(5 + 2n) = 0 Multiply (-1 + 3n) * (5 + 2n) (-1(5 + 2n) + 3n * (5 + 2n)) = 0 ((5 * -1 + 2n * -1) + 3n * (5 + 2n)) = 0 ((-5 + -2n) + 3n * (5 + 2n)) = 0 (-5 + -2n + (5 * 3n + 2n * 3n)) = 0 (-5 + -2n + (15n + 6n2)) = 0 Combine like terms: -2n + 15n = 13n (-5 + 13n + 6n2) = 0 Solving -5 + 13n + 6n2 = 0 Solving for variable 'n'. Factor a trinomial. (-5 + -2n)(1 + -3n) = 0Subproblem 1
Set the factor '(-5 + -2n)' equal to zero and attempt to solve: Simplifying -5 + -2n = 0 Solving -5 + -2n = 0 Move all terms containing n to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -2n = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2n = 0 + 5 -2n = 0 + 5 Combine like terms: 0 + 5 = 5 -2n = 5 Divide each side by '-2'. n = -2.5 Simplifying n = -2.5Subproblem 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 = {-2.5, 0.3333333333}
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