<s>[INST] Unable to get matched answer using factorization I have question to solve by factorization.
the question is $$(a+b)x^2 + (a+2b+c)x + (b+c) = 0$$ 
the answer should be $$x = -a, -b.$$
i have done using it 
\begin{align}
(a+b)x^2 + (a+b+b+c)x + (b+c) &= 0 \\
(a+b)x^2 + ((a+b)+(b+c))x + (b+c) &= 0\\
(a+b)x^2 + (a+b)x+(b+c)x + (b+c) &= 0\\
x(a+b)[x+1] +(b+c)[x+1] &= 0\\
(x+1)(x(a+b)+(b+c)) &= 0\\
\\
x+1 &= 0\\
x(a+b)+(b+c) &= 0
\end{align}
 [/INST] Your answers are correct, and the original answer, unfortunately, is wrong; as you found, the roots of the polynomial are $$x=-1,-\frac{b+c}{a+b},$$ assuming $a+b\ne0$. Also, that was some clever factoring you employed!
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