I was solving the problem listed here..

Polynomial x

I understood the logic behind the first line which says that "A root is of multiplicity 1 ==> the polynomial has a root in common with it's own derivative.

But I wasn't able to follow the next where the reply is like this.

Thus the given information tells us that x^4 + x + 6 and 4x^3 + 1 have a common root r. It follows that

0 = 4(r^4 + r + 6) - r(4r^3 + 1) = 3r + 24.

I could not follow the logic behind the line 0 = 4(r^4 + r + 6) - r(4r^3 + 1) = 3r + 24.

I have been searching for the justification behind this step, but have been failing again and again. Can someone throw some light on this?

Thanks