Question 1187429
Check that the following expressions are equivalent using the values

{{{ x }}}= {{{-2}}}, {{{-1}}}, {{{0}}}, {{{1}}}, {{{2}}}.


{{{(12x^2-27)/3 }}} and  {{{-(-2x+3)(2x+3)}}}


use {{{ x =-2}}}


{{{(12(-2)^2-27)/3 }}} ->{{{(12*4-27)/3 }}}->{{{7}}}

and  

{{{(-(-2(-2)+3)(2(-2)+3))}}}->{{{(-(4+3)(-4+3))}}}->{{{(-(4+3)(-1))}}} ->{{{7}}}


 {{{ x =-1}}}


{{{(12(-1)^2-27)/3 }}} ->{{{(12*1-27)/3 }}}->{{{-5}}}

and  

{{{-(-2(-1)+3)(2(-1)+3)}}}->{{{-(2+3)(-2+3)}}}->{{{(-5)(1)}}} ->{{{-5}}}


{{{ x =0}}}


{{{(12(0)^2-27)/3 }}} ->{{{(0-27)/3 }}}->{{{-9}}}

and  

{{{-(-2(0)+3)(2(0)+3)}}}->{{{-(0+3)(0+3)}}}->{{{(-3)(3)}}} ->{{{-9}}}


{{{ x =1}}}


{{{(12(1)^2-27)/3 }}} ->{{{(12*1-27)/3 }}}->{{{-5}}}

and  

{{{-(-2(1)+3)(2(1)+3)}}}->{{{-(-2+3)(2+3)}}}->{{{-(-1)(5)}}} ->{{{-5}}}


{{{ x =2}}}

{{{(12(2)^2-27)/3 }}} ->{{{(12*4-27)/3 }}}->{{{7}}}

and  

{{{-(-2(2)+3)(2(2)+3)}}}->{{{-(-4+3)(4+3)}}}->{{{-(-1)(7)}}} ->{{{7}}}



since results in both expressions for same {{{x}}} value, it proves  the equivalence of the two expressions  

so, {{{(12x^2-27)/3 =-(-2x+3)(2x+3)}}}