Solution - Linear equations with one unknown

Step by step solution :

Step  1  :

Equation at the end of step  1  :

  (3•5s2) +  43s  = 0 

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   15s² + 43s  =   s • (15s + 43) 

Equation at the end of step  3  :

  s • (15s + 43)  = 0 

Step  4  :

Theory - Roots of a product :

 4.1    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 :

 4.2      Solve  :    s = 0 

  Solution is  s = 0

Solving a Single Variable Equation :

 4.3      Solve  :    15s+43 = 0 

 Subtract  43  from both sides of the equation : 
                      15s = -43
Divide both sides of the equation by 15:
                     s = -43/15 = -2.867

Two solutions were found :

1.  s = -43/15 = -2.867
   
2.  s = 0