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\frac{5n^{2}+3n}{2}
Factor out \frac{1}{2}.
n\left(5n+3\right)
Consider 5n^{2}+3n. Factor out n.
\frac{n\left(5n+3\right)}{2}
Rewrite the complete factored expression.
\frac{5n^{2}+3n}{2}
Since \frac{5n^{2}}{2} and \frac{3n}{2} have the same denominator, add them by adding their numerators.