Solve 16m^2-4m(m+3)<0

$$16 m ^ { 2 } - 4 m ( m + 3 ) < 0$$

Solve for m

$$m\in \left(0,1\right)$$

Solution Steps

Multiply -1 and 4 to get -4.

$$16m^{2}-4m\left(m+3\right)<0$$

Use the distributive property to multiply -4m by m+3.

$$16m^{2}-4m^{2}-12m<0$$

Combine 16m^{2} and -4m^{2} to get 12m^{2}.

$$12m^{2}-12m<0$$

Factor out m.

$$12m\left(m-1\right)<0$$

For the product to be negative, m and m-1 have to be of the opposite signs. Consider the case when m is positive and m-1 is negative.

$$m>0 m-1<0$$

The solution satisfying both inequalities is m\in \left(0,1\right).

$$m\in \left(0,1\right)$$

Consider the case when m-1 is positive and m is negative.

$$m-1>0 m<0$$

This is false for any m.

$$m\in \emptyset$$

The final solution is the union of the obtained solutions.

$$m\in \left(0,1\right)$$