SOLUTION: (3x-2)^2-9(3x-2)+18=0 Find real solutions of the equation.

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Question 102954: (3x-2)^2-9(3x-2)+18=0 Find real solutions of the equation.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
%283x-2%29%5E2-9%283x-2%29%2B18=0
Let Y=3x-2
%283x-2%29%5E2-9%283x-2%29%2B18=0
%28Y%29%5E2-9%28Y%29%2B18=0 Substitute.
Factoring this equation,
%28Y-3%29%2A%28Y-6%29=0Factor 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%2B2=3%2B2
3x=5
x=5%2F3
For Y=6,
Y=3x-2=6
3x-2%2B2=6%2B2
3x=8
x=8%2F3
Two solutions : x+=+5%2F3 and x=8%2F3
The substitution helps out by simplifying the multiplication and factoring.
Let's verify one solution:
%283x-2%29%5E2-9%283x-2%29%2B18=0
%283%2A5%2F3-2%29%5E2-9%283%2A5%2F3-2%29%2B18=0
9-27%2B18=0
0=0
True, Good answer.