# How do you solve 3x^3 + 2x = x^4 + 2x?

Jul 4, 2017

$x = 0 \text{ or } x = 3$

#### Explanation:

$\text{rearrange equation and equate to zero}$

$\Rightarrow {x}^{4} - 3 {x}^{3} = 0$

$\Rightarrow {x}^{3} \left(x - 3\right) = 0$

$\text{equate each factor to zero and solve}$

${x}^{3} = 0 \Rightarrow x = 0 \text{ with multiplicity 3}$

$x - 3 = 0 \Rightarrow x = 3 \text{ with multiplicity 1}$