Vector equation in $\mathbb{R^3}$ Let $\vec{a}$ and $\vec{b}$ are non-zero vector in  $\mathbb{R^3}$ which form an angle $30°$. Their length are $|\vec{b}|=\sqrt{3}|\vec{a}|$. How to solve the vector equation?

$$ (\vec{x} \cdot (\vec{a}+\vec{b})) \vec{a} + \vec{x} \times  \vec{b}
 = 2\vec{a}\times  \vec{b}+3 |\vec{a}|^2\vec{b} $$

I've done this:
$$\vec{a}^2\vec{x}+\vec{a}\vec{b}\vec{x} + \vec{x} \times  \vec{b}
 = 2\vec{a}\times  \vec{b}+3 \frac{|\vec{b}|^2}{3}\vec{b}$$
$$\vec{a}^2\vec{x}+|\vec{a}||\vec{b}|\cdot cos (30°)\cdot  \vec{x} + \vec{x} \times  \vec{b}
 = 2\vec{a}\times  \vec{b}+|\vec{b}|^2\vec{b}$$
what i do now? 
Thanks
 A: Vectors don't just multiply together, you can't write $\vec{a}^2\vec{x}$ for $(\vec{x}.\vec{a})\vec{a}$.  Keep track of what is a scalar, and what is a vector.
As Will Nelson suggests, any vector can be written in terms of $\vec{a}$,$\vec{b}$ and $\vec{a}\times\vec{b}$.  When you substitute it in, remember
1) $\vec{a}.(\vec{a}\times\vec{b})=0$
2) $(\vec{a}\times\vec{b})\times\vec{b}$ equals what?
For example, $\vec{x}.(\vec{a}+\vec{b})=c_a\vec{a}.(\vec{a}+\vec{b})+c_b\vec{b}.(\vec{a}+\vec{b})+c_{a\times b}(\vec{a}\times\vec{b}).(\vec{a}+\vec{b})$.   Now $\vec{a}\times\vec{b}$ is perpendicular to both $\vec{a}$ and $\vec{b}$, so the $c_{a\times b}$ term gives zero.  So $\vec{x}.(\vec{a}+\vec{b})=c_a(\vec{a}.\vec{a}+\vec{a}.\vec{b})+c_b(\vec{a}.\vec{b}+\vec{b}.\vec{b})$.
Rearrange the original equation into $$A\vec{a}+B\vec{b}+C\vec{a}\times\vec{b}=\vec{0}$$ where $A$, $B$ and $C$ are scalars that contain Will Nelson's constants $c_a$, $c_b$ and $c_{a\times b}$, as well as $a.a$, $b.b$ and $a.b$. Then each of $A$, $B$ and $C$ must equal zero.  That gives three equations in the variables $c_a$, $c_b$ and $c_{a\times b}$.  Solve them in terms of $a.a$, $a.b$ and $b.b$, and you have $x=c_a\vec{a}+c_b\vec{b}+c_{a\times b}\vec{a}\times\vec{b}$.
