Solution - Factoring binomials using the difference of squares

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "x1"   was replaced by   "x^1". 

Rearrange:

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

                     -45-(9*(x^12))=0 

Step by step solution :

Step  1  :

Equation at the end of step  1  :

  -45 -  32x12  = 0 

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   -9x¹² - 45  =   -9 • (x¹² + 5) 

Trying to factor as a Sum of Cubes :

 3.2      Factoring:  x¹² + 5 

Theory : A sum of two perfect cubes,  a³ + b³ can be factored into  :
             (a+b) • (a²-ab+b²)
Proof  : (a+b) • (a²-ab+b²) =
    a³-a²b+ab²+ba²-b²a+b³ =
    a³+(a²b-ba²)+(ab²-b²a)+b³=
    a³+0+0+b³=
    a³+b³

Check :  5  is not a cube !!
Ruling : Binomial can not be factored as the difference of two perfect cubes

Equation at the end of step  3  :

  -9 • (x12 + 5)  = 0 

Step  4  :

Equations which are never true :

 4.1      Solve :    -9   =  0

This equation has no solution.
A a non-zero constant never equals zero.

Solving a Single Variable Equation :

 4.2      Solve  :    x¹²+5 = 0 

 Subtract  5  from both sides of the equation : 
                      x¹² = -5
                     x  =  12th root of (-5) 

 The equation has no real solutions. It has 12 imaginary, or complex solutions.
 These solutions are x = 12th root of -5.00000

12 solutions were found :