Width of $\mathrm{GL}(6,K)$ with respect to quasi-root elements

We study structure of $\mathrm{GL}(6,K)$ with respect to a certain family of conjugacy classes, whose elements are called quasi-root. Namely, we prove that any element of $\mathrm{GL}(6,K)$ is a product of three quasi-root elements, and completely describe the elements that are products of two quasi-root elements. The result arises in the study of width of exceptional groups of type $E_6$, but also is of independent interest.