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Final result : (2x + 1) • (x + 3) • (x - 3)

Step by step solution :Step  1  :Equation at the end of step  1  : ((2x2 + 7x) + 3) • (x - 3) Step  2  :Trying to factor by splitting the middle term

 2.1     Factoring  2x2+7x+3 

The first term is,  2x2  its coefficient is  2 .
The middle term is,  +7x  its coefficient is  7 .
The last term, "the constant", is  +3 

Step-1 : Multiply the coefficient of the first term by the constant   2 • 3 = 6 

Step-2 : Find two factors of  6  whose sum equals the coefficient of the middle term, which is   7 .

     -6   +   -1   =   -7     -3   +   -2   =   -5     -2   +   -3   =   -5     -1   +   -6   =   -7     1   +   6   =   7   That's it


Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  1  and  6 
                     2x2 + 1x + 6x + 3

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (2x+1)
              Add up the last 2 terms, pulling out common factors :
                    3 • (2x+1)
Step-5 : Add up the four terms of step 4 :
                    (x+3)  •  (2x+1)
             Which is the desired factorization

Final result : (2x + 1) • (x + 3) • (x - 3)

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