Let $g_i$ denote the $i$'th orthonormal basis of a Clifford algebra $G_{p,q}$, then any number in Clifford domain can be represented as follows: $$a=\sum_{i=1}^{2^{p+q}}(a_ig_{i})$$ where $a_i$ is some real coefficient.
Given Clifford numbers $a,b\in G_{p,q}$ how can I in general solve the following equation for the Clifford number $x=\sum_{i=1}^{2^{p+q}}(x_ig_{i})$, $x \in G_{p,q}$,?
$$(\sum_{i=1}^{2^{p+q}}(x_i(g_{i})^3))(-b)x = (\sum_{i=1}^{2^{p+q}}(a_i(g_{i})^3))ba$$