Solution - Linear equations with one unknown

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "56.5" was replaced by "(565/10)".

Rearrange:

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

                4*(q+(565/10))-(30*q-112)=0 

Step by step solution :

Step  1  :

            113
 Simplify   ———
             2 

Equation at the end of step  1  :

             113      
  (4 • (q +  ———)) -  (30q - 112)  = 0 
              2       

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Adding a fraction to a whole

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

          q     q • 2
     q =  —  =  —————
          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:

 q • 2 + 113     2q + 113
 ———————————  =  ————————
      2             2    

Equation at the end of step  2  :

       (2q + 113)     
  (4 • ——————————) -  (30q - 112)  = 0 
           2          

Step  3  :

Equation at the end of step  3  :

  2 • (2q + 113) -  (30q - 112)  = 0 

Step  4  :

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   338 - 26q  =   -26 • (q - 13) 

Equation at the end of step  5  :

  -26 • (q - 13)  = 0 

Step  6  :

Equations which are never true :

 6.1      Solve :    -26   =  0

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

Solving a Single Variable Equation :

 6.2      Solve  :    q-13 = 0 

 Add  13  to both sides of the equation : 
                      q = 13

One solution was found :