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 :

                     4/5*d+3-(-2-1/5*d)=0 

Step by step solution :

Step  1  :

            1
 Simplify   —
            5

Equation at the end of step  1  :

    4            1
  ((—•d)+3)-(-2-(—•d))  = 0 
    5            5

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  5  as the denominator :

           -2     -2 • 5
     -2 =  ——  =  ——————
           1        5   

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:

 -2 • 5 - (d)     -d - 10
 ————————————  =  ———————
      5              5   

Equation at the end of step  2  :

    4               (-d - 10)
  ((— • d) +  3) -  —————————  = 0 
    5                   5    

Step  3  :

            4
 Simplify   —
            5

Equation at the end of step  3  :

    4               (-d - 10)
  ((— • d) +  3) -  —————————  = 0 
    5                   5    

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  5  as the denominator :

         3     3 • 5
    3 =  —  =  —————
         1       5  

Adding fractions that have a common denominator :

 4.2       Adding up the two equivalent fractions

 4d + 3 • 5     4d + 15
 ——————————  =  ———————
     5             5   

Equation at the end of step  4  :

  (4d + 15)    (-d - 10)
  ————————— -  —————————  = 0 
      5            5    

Step  5  :

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   -d - 10  =   -1 • (d + 10) 

Adding fractions which have a common denominator :

 6.2       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:

 (4d+15) - ((-d-10))     5d + 25
 ———————————————————  =  ———————
          5                 5   

Step  7  :

Pulling out like terms :

 7.1     Pull out like factors :

   5d + 25  =   5 • (d + 5) 

Equation at the end of step  7  :

  d + 5  = 0 

Step  8  :

Solving a Single Variable Equation :

 8.1      Solve  :    d+5 = 0 

 Subtract  5  from both sides of the equation : 
                      d = -5

One solution was found :