$1) 5(x-1)+7x=2$
$⇔5x-5+7x=2$
$⇔12x=2+5$
$⇔12x=7$
$⇔x=\frac{7}{12}$
$2) (x-2)²+4(x-3)=x²+x-3$
$⇔x²-2x.2+2²+4x-12=x²+x-3$
$⇔x²-4x+4x-x²-x=-3+12-4$
$⇔-x=5$
$⇔x=-5$
$3) 10-3(x-2)=2(x+3)-5$
$⇔10-3x+6=2x+6-5$
$⇔-3x-2x=6-5-6-10$
$⇔-5x=-15$
$⇔x=3$
$4) x(2x-1)-2x²=5(x-3)$
$⇔2x²-x-2x²=5x-15$
$⇔-x-5x=-15$
$⇔-6x=-15$
$⇔x=\frac{5}{2}$
$5) \frac{x-7}{2}=\frac{2x-1}{3}$
$⇔3(x-7)=2(2x-1)$
$⇔3x-21=4x-2$
$⇔3x-4x=-2+21$
$⇔-x=19$
$⇔x=-19$
$6) \frac{x+1}{3}-\frac{2x-3}{2}=\frac{x-2}{6}$
$⇔2(x+1)-3(2x-3)=x-2$
$⇔2x+2-6x+9=x-2$
$⇔2x-6x-x=-2-9-2$
$⇔-5x=-13$
$⇔x=\frac{13}{5}$
$7)\frac{2x-1}{3}+\frac{3x-2}{4}=\frac{4x-3}{5}$
$⇔20(2x-1)+15(3x-2)=12(4x-3)$
$⇔40x-20+45x-30=48x-36$
$⇔40x+45x-48x=-36+30+20$
$⇔37x=14$
$⇔x=\frac{14}{37}$
$9) 5x(x-3)-(x-3)=0$
$⇔(5x-1)(x-3)=0$
$⇔\left \{ {{5x-1=0} \atop {x-3=0}} \right.$
$⇔\left \{ {{5x=1} \atop {x=3}} \right.$
$⇔\left \{ {{x=\frac{1}{5}} \atop {x=3}} \right.$
$10) x²-1=(x+1)(3x-5)$
$⇔(x-1)(x+1)-(x+1)(3x-5)=0$
$⇔[(x-1)-(3x-5)](x+1)=0$
$⇔(x-1-3x+5)(x+1)=0$
$⇔(4-2x)(x+1)=0$
$⇔2(2-x)(x+1)=0$
$⇔\left \{ {{2-x=0} \atop {x+1=0}} \right.$
$⇔\left \{ {{x=2} \atop {x=-1}} \right.$
$11) (x-3)²=4$
$⇔(x-3)²-4=0$
$⇔(x-3)²-2²=0$
$⇔(x-3-2)(x-3+2)=0$
$⇔(x-5)(x-1)=0$
$⇔\left \{ {{x-5=0} \atop {x-1=0}} \right.$
$⇔\left \{ {{x=5} \atop {x=1}} \right.$
$12) (2x-1)²-25=0$
$⇔(2x-1)²-5²=0$
$⇔(2x-1-5)(2x-1+5)=0$
$⇔(2x-6)(2x+4)=0$
$⇔\left \{ {{2x-6=0} \atop {2x+4=0}} \right.$
$⇔\left \{ {{2x=6} \atop {2x=-4}} \right.$
$⇔\left \{ {{x=3} \atop {x=-2}} \right.$
