Question

Solve : $3(2x-1{)}^2+4(2x-1)-4=0$

Answer 1

$3{(2x-1)}^2+4(2x-1)-4=0$

say $t=2x-1$, then

$\Rightarrow {3t}^2+4t-4=0$

$\Rightarrow {3t}^2+6t-2t-4=0$

$\Rightarrow 3t(t+2)-2(t+2)=0$

$\Rightarrow (3t-2)(t+2)=0$

$\therefore$ $t=\frac{2}{3}$ or $t=-2$

$\Rightarrow 2x-1=\frac{2}{3}$ or $2x-1=-2$

$\Rightarrow x=\frac{5}{6}$ or $2x=-1$

$\therefore$ $x=1/2$ or $5/6$ or $x=-1/2$