Fill in the missing justification in the following algebraic proof

given: 4(x-8)=2x+12
prove: x=22

statement reason
4(x-8)=2x +12 given
4x-32=2x+12
2x-32=12
2x=44
x=22

Here is the algebraic method for proving that x is 22. See attachment.

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.