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Simplifying (3n + -5)(n + -2) = 0 Reorder the terms: (-5 + 3n)(n + -2) = 0 Reorder the terms: (-5 + 3n)(-2 + n) = 0 Multiply (-5 + 3n) * (-2 + n) (-5(-2 + n) + 3n * (-2 + n)) = 0 ((-2 * -5 + n * -5) + 3n * (-2 + n)) = 0 ((10 + -5n) + 3n * (-2 + n)) = 0 (10 + -5n + (-2 * 3n + n * 3n)) = 0 (10 + -5n + (-6n + 3n2)) = 0 Combine like terms: -5n + -6n = -11n (10 + -11n + 3n2) = 0 Solving 10 + -11n + 3n2 = 0 Solving for variable 'n'. Factor a trinomial. (5 + -3n)(2 + -1n) = 0Subproblem 1
Set the factor '(5 + -3n)' equal to zero and attempt to solve: Simplifying 5 + -3n = 0 Solving 5 + -3n = 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 + -3n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3n = 0 + -5 -3n = 0 + -5 Combine like terms: 0 + -5 = -5 -3n = -5 Divide each side by '-3'. n = 1.666666667 Simplifying n = 1.666666667Subproblem 2
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 = 2Solution
n = {1.666666667, 2}
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