#### Answer

The solutions are $x=-\dfrac{3}{8}\pm\dfrac{\sqrt{41}}{8}$

#### Work Step by Step

$(4x-1)(x+2)=4x$
Evaluate the product on the left side:
$4x^{2}+8x-x-2=4x$
Take $4x$ to the left side and simplify:
$4x^{2}+8x-x-4x-2=0$
$4x^{2}+3x-2=0$
Use the quadratic formula to solve this equation. The formula is $x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. In this case, $a=4$, $b=3$ and $c=−2$
Substitute the known values into the formula and evaluate:
$x=\dfrac{-3\pm\sqrt{3^{2}-4(4)(-2)}}{2(4)}=\dfrac{-3\pm\sqrt{9+32}}{8}=...$
$...=\dfrac{-3\pm\sqrt{41}}{8}=-\dfrac{3}{8}\pm\dfrac{\sqrt{41}}{8}$
The solutions are $x=-\dfrac{3}{8}\pm\dfrac{\sqrt{41}}{8}$