Step-by-step explanation:
Equation at the end of step 1
(3x2 - 38x) + 24 = 0 
STEP2:Trying to factor by splitting the middle term
 2.1     Factoring  3x2-38x+24 
The first term is,  3x2  its coefficient is  3 .
The middle term is,  -38x  its coefficient is  -38 .
The last term, "the constant", is  +24 
Step-1 : Multiply the coefficient of the first term by the constant   3 • 24 = 72 
Step-2 : Find two factors of  72  whose sum equals the coefficient of the middle term, which is   -38 .
     -72   +   -1   =   -73     -36   +   -2   =   -38   That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -36  and  -2 
                     3x2 - 36x - 2x - 24
Step-4 : Add up the first 2 terms, pulling out like factors :
                    3x • (x-12)
              Add up the last 2 terms, pulling out common factors :
                    2 • (x-12)
Step-5 : Add up the four terms of step 4 :
                    (3x-2)  •  (x-12)
             Which is the desired factorization
Equation at the end of step2:
(x - 12) • (3x - 2) = 0 
STEP3:Theory - Roots of a product
 3.1    A product of several terms equals zero. 
 When a product of two or more terms equals zero, then at least one of the terms must be zero. 
 We shall now solve each term = 0 separately 
 In other words, we are going to solve as many equations as there are terms in the product 
 Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation:
 3.2      Solve  :    x-12 = 0 
 Add  12  to both sides of the equation : 
                      x = 12
Solving a Single Variable Equation: