Solution - Linear equations with one unknown

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                     7*k^2-6*k+3-(3)=0 

Step by step solution :

Step  1  :

Equation at the end of step  1  :

  ((7k2 -  6k) +  3) -  3  = 0 

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   7k² - 6k  =   k • (7k - 6) 

Equation at the end of step  3  :

  k • (7k - 6)  = 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  :    7k-6 = 0 

 Add  6  to both sides of the equation : 
                      7k = 6
Divide both sides of the equation by 7:
                     k = 6/7 = 0.857

Two solutions were found :

1.  k = 6/7 = 0.857
   
2.  k = 0