Solving for r - Help with equation

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Hi - I am drawing a comlete blank.
I know I can do the steps to get the answer (6.91%) on calc but want to understand this please.
Solving for r,
$1,000 + $3,165/(1+r) = $25/(1+r) + $4,500/(1+r)2
 
If you multiply everything by (1 + r)2, you’ll have a quadratic equation in r which you can solve using the quadratic formula.
You don’t want to do that. Trust me on this.
 
The C.F. worksheet on the BA II would work wonderfully here and save oodles of time and heartache!!!! Oodles, I tell ya!!!!
 
Yeah I know I’m not going to go about it that way - I’m just struggling with some of the math (forgetting a lot of what I learnt in school)
Thanks.
The solutions on the CFAI site give you the formula and then just skip straight to the answer. They don’t go through the Key strokes or even the method one would use on a Calc. Really bugs me, end up doing a lot of trial and error. I guess this aids my understanding of what to include and exclude on the CF worksheet though. Luckily I’ve got the Wiley Study guide which fills in those blanks.
Thanks for getting back to me.
 
Rearrange the equation and gather like terms. What you have then is an IRR problem.
 
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