Solution - Linear equations with one unknown

Step by step solution :

Step  1  :

Equation at the end of step  1  :

  (12 • (x3)) -  3x2  = 0 
 Step  2  :

Equation at the end of step  2  :

  (22•3x3) -  3x2  = 0 

Step  3  :

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   12x³ - 3x²  =   3x² • (4x - 1) 

Equation at the end of step  4  :

  3x2 • (4x - 1)  = 0 

Step  5  :

Theory - Roots of a product :

 5.1    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 :

 5.2      Solve  :    3x² = 0 

 Divide both sides of the equation by 3:
                     x² = 0
 
 When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:  
                      x  =  ± √ 0  

 Any root of zero is zero. This equation has one solution which is  x = 0

Solving a Single Variable Equation :

 5.3      Solve  :    4x-1 = 0 

 Add  1  to both sides of the equation : 
                      4x = 1
Divide both sides of the equation by 4:
                     x = 1/4 = 0.250

Two solutions were found :

1.  x = 1/4 = 0.250
   
2.  x = 0