(x+1)(x+2)/25=(x+2)(x+3)/12?
12(x2+3x+2)=25(x2+5x+6) by cross-multiplication,
12x2+36x+24=25x2+125x+150 by distribution,
0=13x2+89x+126=(x+2)(13x+63), so x=-2 or x=-63/13.
To convert to pure quadratic:
0=13x2+89x+126=13x2+89x=-126,
x2+89x/13=-126/13,
x2+89x/13+(89/26)2=(89/26)2-126/13=7921/676-126/13=1369/676=(37/26)2,
(x+89/26)2=(37/26)2,
(x+89/26)2-(37/26)2=0 is pure quadratic.
(x+89/26-37/26)(x+89/26+37/26)=0,
x=37/26-89/26=-52/26=-2; x=-(89+37)/26=-126/26=-63/13.