Solve 4p(-p+4)>0

$$4 p ( - p + 4 ) > 0$$

Solve for p

$$p\in \left(0,4\right)$$

Solution Steps

Use the distributive property to multiply 4p by -p+4.

$$4p\left(-p\right)+16p>0$$

Multiply 4 and -1 to get -4.

$$-4pp+16p>0$$

Multiply p and p to get p^{2}.

$$-4p^{2}+16p>0$$

Multiply the inequality by -1 to make the coefficient of the highest power in -4p^{2}+16p positive. Since -1 is negative, the inequality direction is changed.

$$4p^{2}-16p<0$$

Factor out p.

$$4p\left(p-4\right)<0$$

For the product to be negative, p and p-4 have to be of the opposite signs. Consider the case when p is positive and p-4 is negative.

$$p>0 p-4<0$$

The solution satisfying both inequalities is p\in \left(0,4\right).

$$p\in \left(0,4\right)$$

Consider the case when p-4 is positive and p is negative.

$$p-4>0 p<0$$

This is false for any p.

$$p\in \emptyset$$

The final solution is the union of the obtained solutions.

$$p\in \left(0,4\right)$$