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Simplifying 12n2 + 136n + 320 = 0 Reorder the terms: 320 + 136n + 12n2 = 0 Solving 320 + 136n + 12n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '4'. 4(80 + 34n + 3n2) = 0 Factor a trinomial. 4((8 + n)(10 + 3n)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(8 + n)' equal to zero and attempt to solve: Simplifying 8 + n = 0 Solving 8 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + n = 0 + -8 n = 0 + -8 Combine like terms: 0 + -8 = -8 n = -8 Simplifying n = -8Subproblem 2
Set the factor '(10 + 3n)' equal to zero and attempt to solve: Simplifying 10 + 3n = 0 Solving 10 + 3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + 3n = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 3n = 0 + -10 3n = 0 + -10 Combine like terms: 0 + -10 = -10 3n = -10 Divide each side by '3'. n = -3.333333333 Simplifying n = -3.333333333Solution
n = {-8, -3.333333333}
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