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 :

                     13*x^2-16*x-(x^2-x)=0 

Step by step solution :

Step  1  :

Equation at the end of step  1  :

  (13x2 -  16x) -  (x2 - x)  = 0 

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   12x² - 15x  =   3x • (4x - 5) 

Equation at the end of step  3  :

  3x • (4x - 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  :    3x = 0 

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

Solving a Single Variable Equation :

 4.3      Solve  :    4x-5 = 0 

 Add  5  to both sides of the equation : 
                      4x = 5
Divide both sides of the equation by 4:
                     x = 5/4 = 1.250

Two solutions were found :

1.  x = 5/4 = 1.250
   
2.  x = 0