Solution - Linear equations with one unknown

Step by step solution :

Step  1  :

Equation at the end of step  1  :

  (32•5n2) +  10n  = 0 

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   45n² + 10n  =   5n • (9n + 2) 

Equation at the end of step  3  :

  5n • (9n + 2)  = 0 

Step  4  :

Theory - Roots of a product :

 4.1    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 :

 4.2      Solve  :    5n = 0 

 Divide both sides of the equation by 5:
                     n = 0

Solving a Single Variable Equation :

 4.3      Solve  :    9n+2 = 0 

 Subtract  2  from both sides of the equation : 
                      9n = -2
Divide both sides of the equation by 9:
                     n = -2/9 = -0.222

Two solutions were found :

1.  n = -2/9 = -0.222
   
2.  n = 0