Solution - Linear equations with one unknown

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "x6"   was replaced by   "x^6".  5 more similar replacement(s).

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                6*x^6*x^6*x^6*x^6*x^6*x^6-(6*x)=0 

Step by step solution :

Step  1  :

Equation at the end of step  1  :

  ((((((2•3x6)•x6)•x6)•x6)•x6)•x6)-6x  = 0 
 Step  2  :
 Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   6x³⁶ - 6x  =   6x • (x³⁵ - 1) 

Equation at the end of step  3  :

  6x • (x35 - 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  :    6x = 0 

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

Solving a Single Variable Equation :

 4.3      Solve  :    x³⁵-1 = 0 

 Add  1  to both sides of the equation : 
                      x³⁵ = 1
                     x  =  35th root of (1) 

 The equation has one real solution
This solution is  x =

Two solutions were found :

1.  x =
2.  x = 0