24n^2+136n+160=0

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Solution for 24n^2+136n+160=0 equation:


Simplifying
24n2 + 136n + 160 = 0

Reorder the terms:
160 + 136n + 24n2 = 0

Solving
160 + 136n + 24n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '8'.
8(20 + 17n + 3n2) = 0

Factor a trinomial.
8((4 + n)(5 + 3n)) = 0

Ignore the factor 8.

Subproblem 1

Set the factor '(4 + n)' equal to zero and attempt to solve: Simplifying 4 + n = 0 Solving 4 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + n = 0 + -4 n = 0 + -4 Combine like terms: 0 + -4 = -4 n = -4 Simplifying n = -4

Subproblem 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 = -1.666666667

Solution

n = {-4, -1.666666667}

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