Solution - Linear equations with one unknown

Step by step solution :

Step  1  :

Equation at the end of step  1  :

  3x2 -  5x  = 0 

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   3x² - 5x  =   x • (3x - 5) 

Equation at the end of step  3  :

  x • (3x - 5)  = 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  :    x = 0 

  Solution is  x = 0

Solving a Single Variable Equation :

 4.3      Solve  :    3x-5 = 0 

 Add  5  to both sides of the equation : 
                      3x = 5
Divide both sides of the equation by 3:
                     x = 5/3 = 1.667

Two solutions were found :

1.  x = 5/3 = 1.667
   
2.  x = 0