Solution - Linear equations with one unknown

Step by step solution :

Step  1  :

Equation at the end of step  1  :

  z -  23z2  = 0 

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   z - 8z²  =   -z • (8z - 1) 

Equation at the end of step  3  :

  -z • (8z - 1)  = 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  :    -z = 0 

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

Solving a Single Variable Equation :

 4.3      Solve  :    8z-1 = 0 

 Add  1  to both sides of the equation : 
                      8z = 1
Divide both sides of the equation by 8:
                     z = 1/8 = 0.125

Two solutions were found :

1.  z = 1/8 = 0.125
   
2.  z = 0