Yes, I know, Xhin, it's not easy even as a degree 4 equation. I believe however that there are methods for dealing with them. I'm familiar with degree 3, but degree 4 have a method which I haven't looked up. In any case, for the quartic equation above it's better not to multiply it all out but instead write it as two solvable quadratic equations like this:

\( (6x−1)(4x−1) = a \)

\( (12x−1)(3x−1) = b \)

where you have \(ab=7\). This might make the problem more wieldy.

Black Yoshi, I don't think factoring by grouping works in this case since the roots turn out to involve radicals and complex numbers , but you can try it.

Posted January 20th, 2018
by The Fly