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 :

                     8*x^2-19*x-(2*x^2-x)=0 

Step by step solution :

Step  1  :

Equation at the end of step  1  :

  ((8 • (x2)) -  19x) -  (2x2 -  x)  = 0 
 Step  2  :

Equation at the end of step  2  :

  (23x2 -  19x) -  (2x2 - x)  = 0 

Step  3  :

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   6x² - 18x  =   6x • (x - 3) 

Equation at the end of step  4  :

  6x • (x - 3)  = 0 

Step  5  :

Theory - Roots of a product :

 5.1    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 :

 5.2      Solve  :    6x = 0 

 Divide both sides of the equation by 6:
                     x = 0

Solving a Single Variable Equation :

 5.3      Solve  :    x-3 = 0 

 Add  3  to both sides of the equation : 
                      x = 3

Two solutions were found :

1.  x = 3
2.  x = 0