Let's say you have this equation in standard form: 

y=-3x²+24x+5

y=(-3x²+24x)+5 So you would first                put brackets                      around the x² and                x terms. 

y=-3(x²-8x)+5  You would next                    common factor out                a number if you                  can but you would                never common                      factor out an "x".                If there is a                    negative sign you                would always                      common factor that                out.

y=(-3(x²-8x+16)-16)+5 

 

The step above is the hardest step where you have to put brackets before the "-3" and then you would take the middle term of the equation (in this case -8) divide it by 2 and then sqaure it (it will always be postive because when you square a negative or a positive number it would be positive) which in this case equals to 16 so you would add that as the last term in the expression inside the brackets. After that you would add a negative 16 outside of the brackets to make the equation even and then you would close the last bracket.  Then you would add the last term of the original equation.  

 

y=-3(x-4)²+48+5

 

Now in this step you would write the trinomial(x²-8x+16) as a binomial squared(x-4)². Then you would drop the brackets around the -16 and when you do so the -16 should be multiplied by -3 which will result to 48 and then you would add the last term of the original equation.  

 

y=-3(x-4)²+53 In this step you                 just add the last                 terms and you will               have the equation                 in vertex form.