Solution - Factoring multivariable polynomials

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "g3"   was replaced by   "g^3". 

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                     l*g*(x-2)-((l*g^3)^2)=0 

Step by step solution :

Step  1  :

Equation at the end of step  1  :

  lg • (x - 2) -  l2g6  = 0 

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   -l²g⁶ + lgx - 2lg  =   -lg • (lg⁵ - x + 2) 

Trying to factor a multi variable polynomial :

 3.2    Factoring    lg⁵ - x + 2 

Try to factor this multi-variable trinomial using trial and error 

 Factorization fails

Equation at the end of step  3  :

  -lg • (lg5 - x + 2)  = 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   -lg  = 0

Setting any of the variables to zero solves the equation:

 l  =  0
 g  =  0

Solving a Single Variable Equation :

 4.3     Solve   lg⁵-x+2  = 0

In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.

We shall not handle this type of equations at this time.

Two solutions were found :

1.  g  =  0
2.  l  =  0