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Simplifying (3n + -5)(n + 3) = 0 Reorder the terms: (-5 + 3n)(n + 3) = 0 Reorder the terms: (-5 + 3n)(3 + n) = 0 Multiply (-5 + 3n) * (3 + n) (-5(3 + n) + 3n * (3 + n)) = 0 ((3 * -5 + n * -5) + 3n * (3 + n)) = 0 ((-15 + -5n) + 3n * (3 + n)) = 0 (-15 + -5n + (3 * 3n + n * 3n)) = 0 (-15 + -5n + (9n + 3n2)) = 0 Combine like terms: -5n + 9n = 4n (-15 + 4n + 3n2) = 0 Solving -15 + 4n + 3n2 = 0 Solving for variable 'n'. Factor a trinomial. (-3 + -1n)(5 + -3n) = 0Subproblem 1
Set the factor '(-3 + -1n)' equal to zero and attempt to solve: Simplifying -3 + -1n = 0 Solving -3 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1n = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1n = 0 + 3 -1n = 0 + 3 Combine like terms: 0 + 3 = 3 -1n = 3 Divide each side by '-1'. n = -3 Simplifying n = -3Subproblem 2
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 = 1.666666667Solution
n = {-3, 1.666666667}
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