SOLUTION: (x+5)(x+3)+5x+25=0 by factoring

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Question 344967: (x+5)(x+3)+5x+25=0 by factoring
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%2B5%29%28x%2B3%29%2B5x%2B25=0
The long way:
Simplify the left side:
x%5E2+%2B8x+%2B15+%2B+5x+%2B+25+=+0
x%5E2+%2B+13x+%2B+40+=+0
Factor:
%28x%2B8%29%28x%2B5%29+=+0
Solve:
From the Zero Product property we know that one of the factors must be zero:
x%2B8+=+0 or x%2B5+=+0
Solving these we get:
x+=+-8 or x+=+-5

%28x%2B5%29%28x%2B3%29%2B5x%2B25=0
The short way is based on noticing that (x+5) is already a factor of (x+5)(x+3) and that it is also a factor of 5x+25. This means we can factor by grouping:
%28x%2B5%29%28x%2B3%29%2B5%28x%2B5%29+=+0
%28x%2B5%29%28%28x%2B3%29%2B5%29+=+0
%28x%2B5%29%28x%2B8%29+=+0
And the rest is the same as the above.