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 :

                     (5-3*y)^2+y^2-(25)=0 

Step by step solution :

Step  1  :

Step  2  :

Pulling out like terms :

 2.1     Pull out like factors :

   10y² - 30y  =   10y • (y - 3) 

Equation at the end of step  2  :

  10y • (y - 3)  = 0 

Step  3  :

Theory - Roots of a product :

 3.1    A product of several terms equals zero. 

 When a product of two or more terms equals zero, then at least one of the terms must be zero. 

 We shall now solve each term = 0 separately 

 In other words, we are going to solve as many equations as there are terms in the product 

 Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

 3.2      Solve  :    10y = 0 

 Divide both sides of the equation by 10:
                     y = 0

Solving a Single Variable Equation :

 3.3      Solve  :    y-3 = 0 

 Add  3  to both sides of the equation : 
                      y = 3

Two solutions were found :

1.  y = 3
2.  y = 0