#9x^2 + 6x + 1 = 12x#
subtract #12x# from both sides
#9x^2 + 6x + 1 - 12x= 0#
#color(red)"6x - 12x"#
#9x^2 color(red)"- 6x" + 1 = 0#
then my way that I use when the coefficient of #x^2# not #1#
that I multiply the constant by the coefficient of #x^2# then I try to find two numbers that their product equals to the coefficient of #x^2# and their sum equals to the coefficient of #x#.
like here for example
#9x^2 - 6x + 1= 0#
#9*1=9#
so the two numbers are #-3# and #-3#
their product = 9 and their sum = -6
so then I put them in #color(red)"-6x"# place
#9x^2 color(red)"- 3x - 3x" + 1= 0#
the by grouping take the common factor
#color(red)"9x^2 - 3x" color(blue)" - 3x + 1= 0"#
#3x(3x-1)-(3x-1)=0#
so
#(3x-1)(3x-1) = 0#
#(3x-1)^2=0#
square root both sides
#3x-1 = 0#
add 1 to both sides
#3x = 1#
divide both sides by 3
#x = 1/3#
