Question

Solve equations using factorization method:

$4(2x-3{)}^2-(2x-3)-14=0$

Answer 1

Step: Factorising the equation:

$4(2x-3{)}^2-(2x-3)-14=0$

Let $2x-3=y$

$\Rightarrow 4y^2-y-14=0$
$\Rightarrow 4y^2-8y+7y-14=0$ {factorizing left hand side}
$\Rightarrow 4y(y-2)+7(y-2)=0$

$\Rightarrow (y-2)(4y+7)=0$

$\Rightarrow y-2=0or4y+7=0$

{Zero product rule}

$\Rightarrow$ $y=-2$ or $y=\frac{-7}{4}$ as $y=2x-3$

so $2x-3=2$ or $2x-3$ $=\frac{-7}{4}$

$\Rightarrow$ $2x=5$ or $2x$ = $\frac{5}{4}$

$\therefore$ $x=\frac{5}{2}$ or $x=$ $\frac{5}{8}$

Hence, the required answer is $x=\frac{5}{2}$ or x =$\frac{5}{8}$