Answer:
Step-by-step explanation:
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 p2-5p-24=0  
Two solutions were found :
     p = 8
     p = -3  
Reformatting the input :
Changes made to your input should not affect the solution:
 (1): "p2"   was replaced by   "p^2".  
Step by step solution :
Step  1  :
Trying to factor by splitting the middle term
 1.1     Factoring  p2-5p-24  
The first term is,  p2  its coefficient is  1 .
The middle term is,  -5p  its coefficient is  -5 .
The last term, "the constant", is  -24  
Step-1 : Multiply the coefficient of the first term by the constant   1 • -24 = -24  
Step-2 : Find two factors of  -24  whose sum equals the coefficient of the middle term, which is   -5 .
      	-24     +    	1     =    	-23  
      	-12     +    	2     =    	-10  
      	-8     +    	3     =    	-5     That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -8  and  3  
                     p2 - 8p + 3p - 24
Step-4 : Add up the first 2 terms, pulling out like factors :
                    p • (p-8)
              Add up the last 2 terms, pulling out common factors :
                    3 • (p-8)
Step-5 : Add up the four terms of step 4 :
                    (p+3)  •  (p-8)
             Which is the desired factorization
Equation at the end of step  1  :
  (p + 3) • (p - 8)  = 0  
Step  2  :
Theory - Roots of a product :
 2.1    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 :
 2.2      Solve  :    p+3 = 0  
 Subtract  3  from both sides of the equation :  
                      p = -3
Solving a Single Variable Equation :
 2.3      Solve  :    p-8 = 0  
 Add  8  to both sides of the equation :  
                      p = 8