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 :

                     6*x^2-2*x-(x)=0 

Step by step solution :

Step  1  :

Equation at the end of step  1  :

  ((2•3x2) -  2x) -  x  = 0 

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   6x² - 3x  =   3x • (2x - 1) 

Equation at the end of step  3  :

  3x • (2x - 1)  = 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  :    3x = 0 

 Divide both sides of the equation by 3:
                     x = 0

Solving a Single Variable Equation :

 4.3      Solve  :    2x-1 = 0 

 Add  1  to both sides of the equation : 
                      2x = 1
Divide both sides of the equation by 2:
                     x = 1/2 = 0.500

Two solutions were found :

1.  x = 1/2 = 0.500
   
2.  x = 0