Solve (x-6)(x+2)geq0

$$(x-6)(x+2) \geq 0$$

Solve for x

$$x\in (-\infty,-2]\cup [6,\infty)$$

Solution Steps

For the product to be ≥0, x+2 and x-6 have to be both ≤0 or both ≥0. Consider the case when x+2 and x-6 are both ≤0.

$$x+2\leq 0 x-6\leq 0$$

The solution satisfying both inequalities is x\leq -2.

$$x\leq -2$$

Consider the case when x+2 and x-6 are both ≥0.

$$x-6\geq 0 x+2\geq 0$$

The solution satisfying both inequalities is x\geq 6.

$$x\geq 6$$

The final solution is the union of the obtained solutions.

$$x\leq -2\text{; }x\geq 6$$