Answer
$x=\left\{ \dfrac{2-\sqrt{10}}{3},\dfrac{2+\sqrt{10}}{3} \right\}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
(3x+2)(x-1)=3x
,$ 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}
3x(x)+3x(-1)+2(x)+2(-1)=3x
\\\\
3x^2-3x+2x-2=3x
\\\\
3x^2+(-3x+2x-3x)-2=0
\\\\
3x^2-4x-2=0
.\end{array}
In the equation above, $a=
3
,$ $b=
-4
,$ 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{-(-4)\pm\sqrt{(-4)^2-4(3)(-2)}}{2(3)}
\\\\
x=\dfrac{4\pm\sqrt{16+24}}{6}
\\\\
x=\dfrac{4\pm\sqrt{40}}{6}
.\end{array}
Extracting the perfect square factor of the radicand, the equation above is equivalent to
\begin{array}{l}\require{cancel}
x=\dfrac{4\pm\sqrt{4\cdot10}}{6}
\\\\
x=\dfrac{4\pm\sqrt{(2)^2\cdot10}}{6}
\\\\
x=\dfrac{4\pm2\sqrt{10}}{6}
\\\\
x=\dfrac{2(2\pm\sqrt{10})}{6}
\\\\
x=\dfrac{\cancel2(2\pm\sqrt{10})}{\cancel2(3)}
\\\\
x=\dfrac{2\pm\sqrt{10}}{3}
.\end{array}
The solutions are $
x=\left\{ \dfrac{2-\sqrt{10}}{3},\dfrac{2+\sqrt{10}}{3} \right\}
.$