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