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solutions to:
(3x+5)^2+5(3x+5)+6=0

x = -8/3 = -2.667

 x = -7/3 = -2.333

Step-by-step explanation:

Equation at the end of step  1  :

(((3x + 5)2) + 5 • (3x + 5)) + 6 = 0

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  9x2+45x+56 

The first term is,  9x2  its coefficient is  9 .

The middle term is,  +45x  its coefficient is  45 .

The last term, "the constant", is  +56 

Step-1 : Multiply the coefficient of the first term by the constant   9 • 56 = 504 

Step-2 : Find two factors of  504  whose sum equals the coefficient of the middle term, which is   45 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  21  and  24 

                     9x2 + 21x + 24x + 56

Step-4 : Add up the first 2 terms, pulling out like factors :

                    3x • (3x+7)

              Add up the last 2 terms, pulling out common factors :

                    8 • (3x+7)

Step-5 : Add up the four terms of step 4 :

                    (3x+8)  •  (3x+7)

             Which is the desired factorization

Solve  :    3x+7 = 0 

 Subtract  7  from both sides of the equation : 

                      3x = -7

Divide both sides of the equation by 3:

                     x = -7/3 = -2.333

Solving a Single Variable Equation :

 3.3      Solve  :    3x+8 = 0 

 Subtract  8  from both sides of the equation : 

                      3x = -8

Divide both sides of the equation by 3:

                     x = -8/3 = -2.667

Supplement : Solving Quadratic Equation Directly

Solving  9x2+45x+56  = 0 directly

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step-by-step explanation:

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step-by-step explanation: