Solution - Linear equations with one unknown

Step by step solution :

Step  1  :

Equation at the end of step  1  :

  18q -  2q2  = 0 

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   18q - 2q²  =   -2q • (q - 9) 

Equation at the end of step  3  :

  -2q • (q - 9)  = 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  :    -2q = 0 

 Multiply both sides of the equation by (-1) :  2q = 0


Divide both sides of the equation by 2:
                     q = 0

Solving a Single Variable Equation :

 4.3      Solve  :    q-9 = 0 

 Add  9  to both sides of the equation : 
                      q = 9

Two solutions were found :

1.  q = 9
2.  q = 0