Solve 6x^2+54x<0

$$6 x ^ { 2 } + 54 x < 0$$

Solve for x

$$x\in \left(-9,0\right)$$

Solution Steps

Factor out x.

$$6x\left(x+9\right)<0$$

For the product to be negative, x+9 and x have to be of the opposite signs. Consider the case when x+9 is positive and x is negative.

$$x+9>0 x<0$$

The solution satisfying both inequalities is x\in \left(-9,0\right).

$$x\in \left(-9,0\right)$$

Consider the case when x is positive and x+9 is negative.

$$x>0 x+9<0$$

This is false for any x.

$$x\in \emptyset$$

The final solution is the union of the obtained solutions.

$$x\in \left(-9,0\right)$$