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 :

                     1/2*z+6-(3/2*(z+6))=0 

Step by step solution :

Step  1  :

            3
 Simplify   —
            2

Equation at the end of step  1  :

    1                3
  ((— • z) +  6) -  (— • (z + 6))  = 0 
    2                2

Step  2  :

Equation at the end of step  2  :

    1               3 • (z + 6)
  ((— • z) +  6) -  ———————————  = 0 
    2                    2     

Step  3  :

            1
 Simplify   —
            2

Equation at the end of step  3  :

    1               3 • (z + 6)
  ((— • z) +  6) -  ———————————  = 0 
    2                    2     

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Adding a whole to a fraction

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

         6     6 • 2
    6 =  —  =  —————
         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 :

 4.2       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:

 z + 6 • 2     z + 12
 —————————  =  ——————
     2           2   

Equation at the end of step  4  :

  (z + 12)    3 • (z + 6)
  ———————— -  ———————————  = 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:

 (z+12) - (3 • (z+6))     -2z - 6
 ————————————————————  =  ———————
          2                  2   

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   -2z - 6  =   -2 • (z + 3) 

Equation at the end of step  6  :

  -z - 3  = 0 

Step  7  :

Solving a Single Variable Equation :

 7.1      Solve  :    -z-3 = 0 

 Add  3  to both sides of the equation : 
                      -z = 3
Multiply both sides of the equation by (-1) :  z = -3

One solution was found :