Solve 113n-73n^2<0

$$113 n - 73 n ^ { 2 } < 0$$

Solve for n

$$n\in \left(-\infty,0\right)\cup \left(\frac{113}{73},\infty\right)$$

Solution Steps

Multiply the inequality by -1 to make the coefficient of the highest power in 113n-73n^{2} positive. Since -1 is negative, the inequality direction is changed.

$$-113n+73n^{2}>0$$

Factor out n.

$$n\left(73n-113\right)>0$$

For the product to be positive, n and n-\frac{113}{73} have to be both negative or both positive. Consider the case when n and n-\frac{113}{73} are both negative.

$$n<0 n-\frac{113}{73}<0$$

The solution satisfying both inequalities is n<0.

$$n<0$$

Consider the case when n and n-\frac{113}{73} are both positive.

$$n-\frac{113}{73}>0 n>0$$

The solution satisfying both inequalities is n>\frac{113}{73}.

$$n>\frac{113}{73}$$

The final solution is the union of the obtained solutions.

$$n<0\text{; }n>\frac{113}{73}$$