(x-3)(4x+1)=0 that is the solution of x

The equation is already factored so, set each factored form to 0. 
(x-3)=0   (4x+1)=0   

Then, solve each equation. 
x-3=0         4x+1=0 
  +3  +3           -1   -1
     
x=3             4x=-1 
                   ---    ---
                    4     4 
                   
                    x=-1/4 

So x could be either 3 or -1/4.