Solution - Linear equations with one unknown

Rearrange:

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

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

Step by step solution :

Step  1  :

            1
 Simplify   —
            3

Equation at the end of step  1  :

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

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  3  as the denominator :

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

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:

 5y • 3 + 1     15y + 1
 ——————————  =  ———————
     3             3   

Equation at the end of step  2  :

                         (15y + 1)
  (2 • (3y + 5)) -  (3 • —————————)  = 0 
                             3    

Step  3  :

Equation at the end of step  3  :

  (2 • (3y + 5)) -  (15y + 1)  = 0 

Step  4  :

Equation at the end of step  4  :

  2 • (3y + 5) -  (15y + 1)  = 0 

Step  5  :

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   9 - 9y  =   -9 • (y - 1) 

Equation at the end of step  6  :

  -9 • (y - 1)  = 0 

Step  7  :

Equations which are never true :

 7.1      Solve :    -9   =  0

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

Solving a Single Variable Equation :

 7.2      Solve  :    y-1 = 0 

 Add  1  to both sides of the equation : 
                      y = 1

One solution was found :