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 :

                     10*x^2-(6*x)=0 

Step by step solution :

Step  1  :

Equation at the end of step  1  :

  (2•5x2) -  6x  = 0 

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   10x² - 6x  =   2x • (5x - 3) 

Equation at the end of step  3  :

  2x • (5x - 3)  = 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  :    2x = 0 

 Divide both sides of the equation by 2:
                     x = 0

Solving a Single Variable Equation :

 4.3      Solve  :    5x-3 = 0 

 Add  3  to both sides of the equation : 
                      5x = 3
Divide both sides of the equation by 5:
                     x = 3/5 = 0.600

Two solutions were found :

1.  x = 3/5 = 0.600
   
2.  x = 0