Solve for $x$ if $4(2x+3{)}^2-(2x+3)-14=0$.

The correct option is A. $x=-\frac{1}{2},-\frac{19}{8}$

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

Substitute $(2x+3)=y$, the given equation reduces to

$4y^2-y-14=0$

Using Middle Term Splitting,

$\Rightarrow$ $4y^2-8y+7y-14=0$

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

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

$\Rightarrow$ $y=\frac{-7}{4}\text{or}y=2$

When $y=-\frac{7}{4}$,

$(2x+3)=-\frac{7}{4}$

$2x=-\frac{7}{4}-3=\frac{-7-12}{4}=-\frac{19}{4}$

$\Rightarrow$ $x=-\frac{19}{8}$

When $y=2$,

$(2x+3)=2$

$2x=-1$

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

Hence, $x=-\frac{1}{2},-\frac{19}{8}$