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 :

                     4*x^29*x-(12*x)=0 

Step by step solution :

Step  1  :

Equation at the end of step  1  :

  (22x29 • x) -  12x  = 0 
 Step  2  :
 Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   4x³⁰ - 12x  =   4x • (x²⁹ - 3) 

Equation at the end of step  3  :

  4x • (x29 - 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  :    4x = 0 

 Divide both sides of the equation by 4:
                     x = 0

Solving a Single Variable Equation :

 4.3      Solve  :    x²⁹-3 = 0 

 Add  3  to both sides of the equation : 
                      x²⁹ = 3
                     x  =  29th root of (3) 

 The equation has one real solution
This solution is  x = 29th root of 3 = 1.0386

Two solutions were found :

1.  x = 29th root of 3 = 1.0386
2.  x = 0