Solving for a Variable in One Equation

Date: 3/18/96 at 20:52:4
From: Anonymous
Subject: Quadratic Equations

Please help!  I need to write the following in standard form 
and solve for the indicated variable:

             (2r+3)(2r-1) = -(3r+1)

     Thank you, 
         Robert

Date: 3/20/96 at 10:56:55
From: Doctor Patrick
Subject: Re: Quadratic Equations

Hi!  

To solve for r we are going to have to set one side of the equation 
to 0.  

To do this we must add the -(3r+1) to both sides.  This gives us 
(2r+3)(2r-1) + (3r+1) = 0 . Unfortunately, we can't do anything with 
the problem until we clear the parentheses.  Once we do this we get 
(4r^2 + 4r - 3) + (3r+1) = 0.  Remove the parentheses:
4r^2 + 4r - 3 + 3r + 1 = 0.  
Now we add like terms and get 4r^2 + 7r - 2 = 0. 

Now all that is left to do is to factor the problem and solve each half 
separately. I'll let you try this part on your own, but write back if 
you need more help.

Good luck!

-Doctor Patrick,  The Math Forum