Solution - Linear equations with one unknown

Step by step solution :

Step  1  :

Step  2  :

Pulling out like terms :

 2.1    Simplify ( 3x-9 )²

Put the exponent aside and simplfy the base by pulling out like factors :
 3x-9  =  3 • (x-3) 

Remember the 4th law of exponents : (a • b)^m= a^m• b^m

Retract the exponent and apply the 4th law to the simplified base: ( 3 • (x-3) )² =  (3)² • (x-3)²  

Equation at the end of step  2  :

  (3)2 • (x - 3)2  = 0 

Step  3  :

Equations which are never true :

 3.1      Solve :    3   =  0

This equation has no solution.
A a non-zero constant never equals zero.

Solving a Single Variable Equation :

 3.2      Solve  :    (x-3)² = 0 

  (x-3) ² represents, in effect, a product of 2 terms which is equal to zero

For the product to be zero, at least one of these terms must be zero. Since all these terms are equal to each other, it actually means :   x-3  = 0

Add  3  to both sides of the equation : 
                      x = 3

One solution was found :