Solution - Linear equations with one unknown

Step by step solution :

Step  1  :

Step  2  :

Pulling out like terms :

 2.1     Pull out like factors :

   14a - a²  =   -a • (a - 14) 

Equation at the end of step  2  :

  -a • (a - 14)  = 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  :    -a = 0 

 Multiply both sides of the equation by (-1) :  a = 0

Solving a Single Variable Equation :

 3.3      Solve  :    a-14 = 0 

 Add  14  to both sides of the equation : 
                      a = 14

Two solutions were found :

1.  a = 14
2.  a = 0