Answer
$d=\frac{1}{2}$ and $d=-\frac{1}{2}$.
Work Step by Step
The given equation is
$\Rightarrow (2-4d)(2+4d)=0$
Use zero-product property rule.
$\Rightarrow 2-4d=0$ or $2+4d=0$
Solve for $d$.
$\Rightarrow 2=4d$ or $4d=-2$
$\Rightarrow \frac{2}{4}=d$ or $d=-\frac{2}{4}$
$\Rightarrow \frac{1}{2}=d$ or $d=-\frac{1}{2}$
Check:-
$d=\frac{1}{2}$
$\Rightarrow (2-4(\frac{1}{2}))(2+4(\frac{1}{2}))=0$
$\Rightarrow (2-2)(2+2)=0$
$\Rightarrow (0)(2+2)=0$
$\Rightarrow 0=0$
True.
Check:-
$d=-\frac{1}{2}$
$\Rightarrow (2-4(-\frac{1}{2}))(2+4(-\frac{1}{2}))=0$
$\Rightarrow (2+2)(2-2)=0$
$\Rightarrow (4)(0)=0$
$\Rightarrow 0=0$
True.
Hence, the solutions are $d=\frac{1}{2}$ and $d=-\frac{1}{2}$.
