|x^2+4x+3|+2x+5=0 solve

Dear akash

|x^2+4x+3|+2x+5=0

|x^2+4x+3| =-(2x+5)

so for solution exists 

 2x+5 ≤0

x≤-2.5

now check for x^2+4x+3≤0

                   (x+3)(x+1)≤0

                       -3 ≤ x≤-1

 case 1      x≤-3

x^2+4x+3 =-(2x+5)

or x^2+6x+8| =0

   x=-4 and -2   

 -2 is not a solution

case 2    -3 <x≤-2.5

-(x^2+4x+3) =-(2x+5)

 x^2+2x-2 =0

 x= -1 ±√3

  so x= -1 -√3  is accepted solution

so final solution is x =-4 and -1-√3

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