Solution - Adding, subtracting and finding the least common multiple

Rearrange:

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

           (15)*(2/3*x+10)-((15)*(x/5+36/5))=0 

Step by step solution :

Step  1  :

            36
 Simplify   ——
            5 

Equation at the end of step  1  :

        2              x 36
  (15•((—•x)+10))-(15•(—+——))  = 0 
        3              5 5 

Step  2  :

            x
 Simplify   —
            5

Equation at the end of step  2  :

        2              x 36
  (15•((—•x)+10))-(15•(—+——))  = 0 
        3              5 5 

Step  3  :

Adding fractions which have a common denominator :

 3.1       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:

 x + 36     x + 36
 ——————  =  ——————
   5          5   

Equation at the end of step  3  :

        2             (x+36)
  (15•((—•x)+10))-(15•——————)  = 0 
        3               5   

Step  4  :

Equation at the end of step  4  :

        2
  (15•((—•x)+10))-3•(x+36)  = 0 
        3

Step  5  :

            2
 Simplify   —
            3

Equation at the end of step  5  :

          2                 
  (15 • ((— • x) +  10)) -  3 • (x + 36)  = 0 
          3                 

Step  6  :

Rewriting the whole as an Equivalent Fraction :

 6.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  3  as the denominator :

          10     10 • 3
    10 =  ——  =  ——————
          1        3   

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 :

 6.2       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:

 2x + 10 • 3     2x + 30
 ———————————  =  ———————
      3             3   

Equation at the end of step  6  :

        (2x + 30)     
  (15 • —————————) -  3 • (x + 36)  = 0 
            3         

Step  7  :

Step  8  :

Pulling out like terms :

 8.1     Pull out like factors :

   2x + 30  =   2 • (x + 15) 

Equation at the end of step  8  :

  10 • (x + 15) -  3 • (x + 36)  = 0 

Step  9  :

Step  10  :

Pulling out like terms :

 10.1     Pull out like factors :

   7x + 42  =   7 • (x + 6) 

Equation at the end of step  10  :

  7 • (x + 6)  = 0 

Step  11  :

Equations which are never true :

 11.1      Solve :    7   =  0

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

Solving a Single Variable Equation :

 11.2      Solve  :    x+6 = 0 

 Subtract  6  from both sides of the equation : 
                      x = -6

One solution was found :