Solution - Linear equations with one unknown

Step by step solution :

Step  1  :

Equation at the end of step  1  :

  32k2 -  4k  = 0 

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   9k² - 4k  =   k • (9k - 4) 

Equation at the end of step  3  :

  k • (9k - 4)  = 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  :    k = 0 

  Solution is  k = 0

Solving a Single Variable Equation :

 4.3      Solve  :    9k-4 = 0 

 Add  4  to both sides of the equation : 
                      9k = 4
Divide both sides of the equation by 9:
                     k = 4/9 = 0.444

Two solutions were found :

1.  k = 4/9 = 0.444
   
2.  k = 0