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Simplifying (3n + -2)(n + 5) = 0 Reorder the terms: (-2 + 3n)(n + 5) = 0 Reorder the terms: (-2 + 3n)(5 + n) = 0 Multiply (-2 + 3n) * (5 + n) (-2(5 + n) + 3n * (5 + n)) = 0 ((5 * -2 + n * -2) + 3n * (5 + n)) = 0 ((-10 + -2n) + 3n * (5 + n)) = 0 (-10 + -2n + (5 * 3n + n * 3n)) = 0 (-10 + -2n + (15n + 3n2)) = 0 Combine like terms: -2n + 15n = 13n (-10 + 13n + 3n2) = 0 Solving -10 + 13n + 3n2 = 0 Solving for variable 'n'. Factor a trinomial. (-5 + -1n)(2 + -3n) = 0Subproblem 1
Set the factor '(-5 + -1n)' equal to zero and attempt to solve: Simplifying -5 + -1n = 0 Solving -5 + -1n = 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 + -1n = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1n = 0 + 5 -1n = 0 + 5 Combine like terms: 0 + 5 = 5 -1n = 5 Divide each side by '-1'. n = -5 Simplifying n = -5Subproblem 2
Set the factor '(2 + -3n)' equal to zero and attempt to solve: Simplifying 2 + -3n = 0 Solving 2 + -3n = 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 + -3n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3n = 0 + -2 -3n = 0 + -2 Combine like terms: 0 + -2 = -2 -3n = -2 Divide each side by '-3'. n = 0.6666666667 Simplifying n = 0.6666666667Solution
n = {-5, 0.6666666667}
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