Answer
$x=\left\{ \dfrac{-3-\sqrt{41}}{8},\dfrac{-3+\sqrt{41}}{8} \right\}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
(4x-1)(x+2)=4x
,$ use the FOIL Method and express the equation in the form $ax^2+bx+c=0.$ Then use the Quadratic Formula.
$\bf{\text{Solution Details:}}$
Using the FOIL Method which is given by $(a+b)(c+d)=ac+ad+bc+bd,$ the expression above is equivalent to\begin{array}{l}\require{cancel}
4x(x)+4x(2)-1(x)-1(2)=4x
\\\\=
4x^2+8x-x-2=4x
\\\\=
4x^2+(8x-x-4x)-2=0
\\\\=
4x^2+3x-2=0
.\end{array}
In the equation above, $a=
4
,$ $b=
3
,$ and $c=
-2
.$ Using the Quadratic Formula which is given by $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a},$ then
\begin{array}{l}\require{cancel}
x=\dfrac{-3\pm\sqrt{3^2-4(4)(-2)}}{2(4)}
\\\\
x=\dfrac{-3\pm\sqrt{9+32}}{8}
\\\\
x=\dfrac{-3\pm\sqrt{41}}{8}
.\end{array}
The solutions are $
x=\left\{ \dfrac{-3-\sqrt{41}}{8},\dfrac{-3+\sqrt{41}}{8} \right\}
.$
