# How do you solve a^3 = 4a ?

Sep 27, 2016

$a = 0$ or $a = - 2$ or $a = 2$

#### Explanation:

${a}^{3} = 4 a$

$\Leftrightarrow {a}^{3} - 4 a = 0$ or

$a \left({a}^{2} - 4\right) = 0$ or

$a \left({a}^{2} - {2}^{2}\right) = 0$ or

$a \left(a + 2\right) \left(a - 2\right) = 0$

Hence either $a = 0$ or $a + 2 = 0$ or $a - 2 = 0$ i.e.

$a = 0$ or $a = - 2$ or $a = 2$