Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "13.5" was replaced by "(135/10)". 2 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 :

                5*c+(165/10)-((135/10)+10*c)=0 

Step by step solution :

Step  1  :

            27
 Simplify   ——
            2 

Equation at the end of step  1  :

         165      27    
  (5c +  ———) -  (—— +  10c)  = 0 
         10       2     

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Adding a whole to a fraction

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

           10c     10c • 2
    10c =  ———  =  ———————
            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 :

 2.2       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:

 27 + 10c • 2     20c + 27
 ————————————  =  ————————
      2              2    

Equation at the end of step  2  :

         165     (20c + 27)
  (5c +  ———) -  ——————————  = 0 
         10          2     

Step  3  :

            33
 Simplify   ——
            2 

Equation at the end of step  3  :

         33     (20c + 27)
  (5c +  ——) -  ——————————  = 0 
         2          2     

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Adding a fraction to a whole

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

           5c     5c • 2
     5c =  ——  =  ——————
           1        2   

Adding fractions that have a common denominator :

 4.2       Adding up the two equivalent fractions

 5c • 2 + 33     10c + 33
 ———————————  =  ————————
      2             2    

Equation at the end of step  4  :

  (10c + 33)    (20c + 27)
  —————————— -  ——————————  = 0 
      2             2     

Step  5  :

Adding fractions which have a common denominator :

 5.1       Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

 (10c+33) - ((20c+27))     6 - 10c
 —————————————————————  =  ———————
           2                  2   

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   6 - 10c  =   -2 • (5c - 3) 

Equation at the end of step  6  :

  3 - 5c  = 0 

Step  7  :

Solving a Single Variable Equation :

 7.1      Solve  :    -5c+3 = 0 

 Subtract  3  from both sides of the equation : 
                      -5c = -3
Multiply both sides of the equation by (-1) :  5c = 3


Divide both sides of the equation by 5:
                     c = 3/5 = 0.600

One solution was found :