Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.75" was replaced by "(75/100)". 2 more similar replacement(s)

Step by step solution :

Step  1  :

            3
 Simplify   —
            4

Equation at the end of step  1  :

               15          3
  20 • ((0 -  (—— • r)) +  —)  = 0 
               10          4

Step  2  :

            3
 Simplify   —
            2

Equation at the end of step  2  :

               3          3
  20 • ((0 -  (— • r)) +  —)  = 0 
               2          4

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       2 

      The right denominator is :       4 

      Least Common Multiple:
      4 

Calculating Multipliers :

 3.2    Calculate multipliers for the two fractions


    Denote the Least Common Multiple by  L.C.M 
    Denote the Left Multiplier by  Left_M 
    Denote the Right Multiplier by  Right_M 
    Denote the Left Deniminator by  L_Deno 
    Denote the Right Multiplier by  R_Deno 

   Left_M = L.C.M / L_Deno = 2

   Right_M = L.C.M / R_Deno = 1

Making Equivalent Fractions :

 3.3      Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example :  1/2   and  2/4  are equivalent,  y/(y+1)²   and  (y²+y)/(y+1)³  are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

   L. Mult. • L. Num.      -3r • 2
   ——————————————————  =   ———————
         L.C.M                4   

   R. Mult. • R. Num.      3
   ——————————————————  =   —
         L.C.M             4

Adding fractions that have a common denominator :

 3.4       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:

 -3r • 2 + 3     3 - 6r
 ———————————  =  ——————
      4            4   

Equation at the end of step  3  :

       (3 - 6r)
  20 • ————————  = 0 
          4    

Step  4  :

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   3 - 6r  =   -3 • (2r - 1) 

Equation at the end of step  5  :

  -15 • (2r - 1)  = 0 

Step  6  :

Equations which are never true :

 6.1      Solve :    -15   =  0

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

Solving a Single Variable Equation :

 6.2      Solve  :    2r-1 = 0 

 Add  1  to both sides of the equation : 
                      2r = 1
Divide both sides of the equation by 2:
                     r = 1/2 = 0.500

One solution was found :