Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "12.5" was replaced by "(125/10)". 3 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 :

           (4/10)*(20-10*m)-((25/10)-2*m-(125/10))=0 

Step by step solution :

Step  1  :

            25
 Simplify   ——
            2 

Equation at the end of step  1  :

    4             25     25
  (——•(20-10m))-((——-2m)-——)  = 0 
   10             10     2 

Step  2  :

            5
 Simplify   —
            2

Equation at the end of step  2  :

    4                    5           25
  (—— • (20 - 10m)) -  ((— -  2m) -  ——)  = 0 
   10                    2           2 

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a whole from a fraction

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

          2m     2m • 2
    2m =  ——  =  ——————
          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:

 5 - (2m • 2)     5 - 4m
 ————————————  =  ——————
      2             2   

Equation at the end of step  3  :

    4                   (5 - 4m)    25
  (—— • (20 - 10m)) -  (———————— -  ——)  = 0 
   10                      2        2 

Step  4  :

Adding fractions which have a common denominator :

 4.1       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:

 (5-4m) - (25)     -4m - 20
 —————————————  =  ————————
       2              2    

Equation at the end of step  4  :

    4                  (-4m - 20)
  (—— • (20 - 10m)) -  ——————————  = 0 
   10                      2     

Step  5  :

            2
 Simplify   —
            5

Equation at the end of step  5  :

   2                  (-4m - 20)
  (— • (20 - 10m)) -  ——————————  = 0 
   5                      2     

Step  6  :

Step  7  :

Pulling out like terms :

 7.1     Pull out like factors :

   20 - 10m  =   -10 • (m - 2) 

Equation at the end of step  7  :

                  (-4m - 20)
  -4 • (m - 2) -  ——————————  = 0 
                      2     

Step  8  :

Rewriting the whole as an Equivalent Fraction :

 8.1   Subtracting a fraction from a whole

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

                     -4 • (m - 2)     -4 • (m - 2) • 2
     -4 • (m - 2) =  ————————————  =  ————————————————
                          1                  2        

Step  9  :

Pulling out like terms :

 9.1     Pull out like factors :

   -4m - 20  =   -4 • (m + 5) 

Adding fractions that have a common denominator :

 9.2       Adding up the two equivalent fractions

 -4 • (m-2) - (-2 • (m+5))     18 - 2m
 —————————————————————————  =  ———————
             1                    1   

Step  10  :

Pulling out like terms :

 10.1     Pull out like factors :

   18 - 2m  =   -2 • (m - 9) 

Equation at the end of step  10  :

  -2 • (m - 9)  = 0 

Step  11  :

Equations which are never true :

 11.1      Solve :    -2   =  0

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

Solving a Single Variable Equation :

 11.2      Solve  :    m-9 = 0 

 Add  9  to both sides of the equation : 
                      m = 9

One solution was found :