Solve -12n+3n^2-3n<0

$$-12n+3 { n }^{ 2 } -3n < 0$$

Solve for n

$$n\in \left(0,5\right)$$

Solution Steps

Combine -12n and -3n to get -15n.

$$-15n+3n^{2}<0$$

Factor out n.

$$3n\left(n-5\right)<0$$

For the product to be negative, n and n-5 have to be of the opposite signs. Consider the case when n is positive and n-5 is negative.

$$n>0 n-5<0$$

The solution satisfying both inequalities is n\in \left(0,5\right).

$$n\in \left(0,5\right)$$

Consider the case when n-5 is positive and n is negative.

$$n-5>0 n<0$$

This is false for any n.

$$n\in \emptyset$$

The final solution is the union of the obtained solutions.

$$n\in \left(0,5\right)$$