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Reformatting the input :

Changes made to your input should not affect the solution:

(1): "1.5" was replaced by "(15/10)".

Rearrange:

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

                36*a-(180-(15/10)*x^180)=0 

Step  1  :

            3
 Simplify   —
            2

Equation at the end of step  1  :

                  3
  36a -  (180 -  (— • x180))  = 0 
                  2

Step  2  :

Equation at the end of step  2  :

                 3x180 
  36a -  (180 -  —————)  = 0 
                   2  

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  2  as the denominator :

            180     180 • 2
     180 =  ———  =  ———————
             1         2   

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

 3.2       Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

 180 • 2 - (3x180)      360 - 3x180 
 —————————————————  =  ———————————
         2                  2     

Equation at the end of step  3  :

         (360 - 3x180) 
  36a -  —————————————  = 0 
               2      

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  2  as the denominator :

            36a     36a • 2
     36a =  ———  =  ———————
             1         2   

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   360 - 3x¹⁸⁰  =   -3 • (x¹⁸⁰ - 120) 

Trying to factor as a Difference of Squares :

 5.2      Factoring:  x¹⁸⁰ - 120 

Theory : A difference of two perfect squares,  A² - B²  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =
         A² - AB + BA - B² =
         A² - AB + AB - B² =
         A² - B²

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 120 is not a square !!

Ruling : Binomial can not be factored as the difference of two perfect squares.

Trying to factor as a Difference of Cubes:

 5.3      Factoring:  x¹⁸⁰ - 120 

Theory : A difference 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 :  120  is not a cube !!
Ruling : Binomial can not be factored as the difference of two perfect cubes

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 36a • 2 - (-3 • (x180-120))      3x180 + 72a - 360 
 ———————————————————————————  =  —————————————————
              2                          2        

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   3x¹⁸⁰ + 72a - 360  =   3 • (x¹⁸⁰ + 24a - 120) 

Trying to factor a multi variable polynomial :

 6.2    Factoring    x¹⁸⁰ + 24a - 120 

Try to factor this multi-variable trinomial using trial and error 

 Factorization fails

Equation at the end of step  6  :

  3 • (x180 + 24a - 120) 
  ——————————————————————  = 0 
            2           

Step  7  :

When a fraction equals zero :

 7.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

  3•(x180+24a-120) 
  ———————————————— • 2 = 0 • 2
         2        

Now, on the left hand side, the  2  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
   3  •  (x¹⁸⁰+24a-120)  = 0

Equations which are never true :

 7.2      Solve :    3   =  0

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

Solving a Single Variable Equation :

 7.3     Solve   x¹⁸⁰+24a-120  = 0

In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.

We shall not handle this type of equations at this time.

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