I'm not sure about a two-column proof, but here's the answer
3x^2-7x+2=0 factor
(3x - 1) (x - 2) = 0 set each factor to 0
3x - 1 = 0 x - 2 = 0
add 1 to each side add 2 to each side
3x = 1 x = 2
divide both sides by 3
x = 1/3
And those are the two solutions
