Question 36349
This is a hard one to factor but it can be done with a bit of trial & error:
The factors of 135 are:
1 X 135 = 135
3 X 45 = 135
5 X 27 = 135
9 X 15 = 135
The factors of 91 are:
1 X 91 = 91
7 X 13 = 91

You can try various combinations of these but the sum (or the difference) of the factors for the x-term must equal -222.
For example:
{{{(15x - 13)(9x - 7) = 135x^2 - 222x + 91}}}
To find the roots, we must have an equation, so you can set the expression equal to zero.
{{{135x^2 - 222x + 91 = 0}}} Factor.
{{{(15x - 13)(9x - 7) = 0}}} Apply the zero products principle.
{{{15x - 13 = 0}}} and/or {{{9x - 7 = 0}}}
If {{{15x - 13 = 0}}} then {{{15x = 13}}} and {{{x = 13/15}}}
If {{{9x - 7 = 0}}} then {{{9x = 7}}} and {{{x = 7/9}}}
The factors are: (15x - 13) and (9x - 7)
The roots are: {{{x = 13/15}}} and {{{x = 7/9}}}