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