Solution - Linear equations with one unknown

Step by step solution :

Step  1  :

Equation at the end of step  1  :

  3d2 +  47d  = 0 

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   3d² + 47d  =   d • (3d + 47) 

Equation at the end of step  3  :

  d • (3d + 47)  = 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  :    d = 0 

  Solution is  d = 0

Solving a Single Variable Equation :

 4.3      Solve  :    3d+47 = 0 

 Subtract  47  from both sides of the equation : 
                      3d = -47
Divide both sides of the equation by 3:
                     d = -47/3 = -15.667

Two solutions were found :

1.  d = -47/3 = -15.667
   
2.  d = 0