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(a+1)(a+2)+(-a-1)(a+3)=0
We add all the numbers together, and all the variables
(a+1)(a+2)+(-1a-1)(a+3)=0
We multiply parentheses ..
(+a^2+2a+a+2)+(-1a-1)(a+3)=0
We get rid of parentheses
a^2+2a+a+(-1a-1)(a+3)+2=0
We multiply parentheses ..
a^2+(-1a^2-3a-1a-3)+2a+a+2=0
We add all the numbers together, and all the variables
a^2+(-1a^2-3a-1a-3)+3a+2=0
We get rid of parentheses
a^2-1a^2-3a-1a+3a-3+2=0
We add all the numbers together, and all the variables
-1a-1=0
We move all terms containing a to the left, all other terms to the right
-a=1
a=1/-1
a=-1
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