How do you find the common root of an equation?

Question

the equation is x^2 - 6x + 5 = 0 and the answer is 2x^2 - 2

How the heck did they get that answer??

Answer 1

Without guessing If have two plynoms P(x) and Q(x)
you make the division of the higher grade polynom with the lower grade on

P(x)=Q(x)*D(x) + R(x). grade R(x) lower than Q(x).
If there are common roots of P and Q they are also roots of R(x).So you can follow on dividing Q into R and find an other remainder R´(x) whose grade is lower than R(x)
So you go on until you find a remainder so you can solve

last remainder found =0.
You must test those roots in P(x) and Q(x) and see if they are common

Answer 2

The roots are when y = 0, or the graph crosses the x axis.
You don't figure out the roots of a function with another. You just need to find where it equals zero.
(x+6)(x-1)=0 The roots are -6 and 1.