Question 102954
{{{(3x-2)^2-9(3x-2)+18=0}}}
Let {{{Y=3x-2}}} 
{{{(3x-2)^2-9(3x-2)+18=0}}}
{{{(Y)^2-9(Y)+18=0}}} Substitute.
Factoring this equation, 
{{{(Y-3)*(Y-6)=0}}}Factor the quadratic equation. 
The solutions are Y=3 and Y=6, but you need answers in x.
For Y=3,
{{{Y=3x-2=3}}}
{{{3x-2+2=3+2}}}
{{{3x=5}}}
{{{x=5/3}}}
For Y=6,
{{{Y=3x-2=6}}}
{{{3x-2+2=6+2}}}
{{{3x=8}}}
{{{x=8/3}}}
Two solutions : {{{x = 5/3}}} and {{{x=8/3}}}
The substitution helps out by simplifying the multiplication and factoring. 
Let's verify one solution:
{{{(3x-2)^2-9(3x-2)+18=0}}}
{{{(3*5/3-2)^2-9(3*5/3-2)+18=0}}}
{{{9-27+18=0}}}
{{{0=0}}}
True, Good answer.