# How do you solve x(x+3)(x-4)=0?

Dec 12, 2016

See explanation.

#### Explanation:

In such examples you can use the following property of real numbers (expressions):

## A product of expressions is zero if and only if any of these expressions is zero.

If you use the property in this example you get:

$x \left(x + 3\right) \left(x - 4\right) = 0 \iff x = 0 \vee x + 3 = 0 \vee x - 4 = 0$

In this way one equation of 3rd degree is changed to 3 linear equations:

After solving them you get the final answer:

$x = 0 \vee x = - 3 \vee x = 4$