SOLUTION: (x-3)(x+7)-(x+1)(x+5)=0 solve for x?

Algebra ->  Equations -> SOLUTION: (x-3)(x+7)-(x+1)(x+5)=0 solve for x?      Log On


   

Question 235768: (x-3)(x+7)-(x+1)(x+5)=0
solve for x?
Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
Given: %28%28X-3%29%2A%28X%2B7%29%29+-+%28%28X%2B1%29%2A%28X%2B5%29%29+=+0
Basically you have 2 problems in 1
--------------------
Solution:
For now lets just look at the first part of the problem
%28%28X-3%29%2A%28X%2B7%29%29
This can be rewritten using the FOIL method.
%28X%5E2%2B7X-3X-21%29 Combine like terms
%28X%5E2%2B4X-21%29
Now lets look at the second section
%28%28X%2B1%29%2A%28X%2B5%29%29
This can also be rewritten using the FOIL method
%28X%5E2%2B5X%2B1X%2B5%29 Combine like terms
%28X%5E2%2B6X%2B5%29
Now plug our simplified equations into the given equation
%28%28X-3%29%2A%28X%2B7%29%29+-+%28%28X%2B1%29%2A%28X%2B5%29%29+=+0
%28X%5E2%2B4X-21%29-%28X%5E2%2B6X%2B5%29+=+0
Notice that the second part of the equation has a negative sign in front of it. That means that we have to swith the signs of everything inside the brackets.
X%5E2%2B4X-21-X%5E2-6X-5+=+0 Combine like terms
-2X-26+=+0 Add 2X to both sides
-26+=+2X Divide both sides by 2
-13+=+X
----------------
Check you answer:
Plug -13 in for X in the given equation
%28%28X-3%29%2A%28X%2B7%29%29+-+%28%28X%2B1%29%2A%28X%2B5%29%29+=+0
%28%28-13-3%29%2A%28-13%2B7%29%29+-+%28%28-13%2B1%29%2A%28-13%2B5%29%29+=+0 Simplify
%28%28-16%29%2A%28-6%29%29+-+%28%28-12%29%2A%28-8%29%29+=+0 Simplify
96+-+96+=+0
0+=+0