# How do you solve the inequality: (x+6)(x-6)>0?

Aug 29, 2015

$x \in \left(- \infty , - 6\right) \cup \left(6 , + \infty\right)$

#### Explanation:

Notice that the left-hand side of the equation is actually a product of two expressions, $\left(x + 6\right)$ and $\left(x - 6\right)$.

In order for this product to be positive, you need both terms to either be positive or either be negative.

For values of $x > 6$ you get that

$\left\{\begin{matrix}x + 6 > 0 \\ x - 6 > 0\end{matrix}\right. \implies \left(x + 6\right) \left(x - 6\right) > 0$

For values of $x < - 6$ you get that

$\left\{\begin{matrix}x + 6 < 0 \\ x - 6 < 0\end{matrix}\right. \implies \left(x + 6\right) \left(x - 6\right) > 0$

This means that any value of $x$ that is smaller than $\left(- 6\right)$ and any value of $x$ that is greater than $6$ will satisfy this inequality. The solution set will thus be $x \in \left(- \infty , - 6\right) \cup \left(6 , + \infty\right)$.