Answer
{$\frac{2 \pm \sqrt (10)}{3}$}
Work Step by Step
Step 1: $(3x+2)(x-1)=3x$
Step 2: $3x(x-1)+2(x-1)=3x$
Step 3: $3x^{2}-3x+2x-2=3x$
Step 4: $3x^{2}-x-2=3x$
Step 5: Subtracting $3x$ from both sides of the equation, $3x^{2}-x-2-3x=3x-3x$
Step 6: $3x^{2}-4x-2=0$
Step 7: Comparing $3x^{2}-4x-2=0$ to the standard form of a quadratic equation $ax^{2}+bx+c=0$;
$a=3$, $b=-4$ and $c=-2$
Step 8: The quadratic formula is:
$x=\frac{-b \pm \sqrt (b^{2}-4ac)}{2a}$
Step 9: Substituting the values of a,b and c in the formula:
$x=\frac{-(-4) \pm \sqrt ((-4)^{2}-4(3)(-2))}{2(3)}$
Step 10: $x=\frac{4 \pm \sqrt (16+24)}{6}$
Step 11: $x=\frac{4 \pm \sqrt (40)}{6}$
Step 12: $x=\frac{4 \pm \sqrt (4\times10)}{6}$
Step 13: $x=\frac{4 \pm 2\sqrt (10)}{6}$
Step 14: $x=\frac{2(2 \pm \sqrt (10))}{6}$
Step 15: $x=\frac{2 \pm \sqrt (10)}{3}$
Step 16: Therefore, the solution set is {$\frac{2 \pm \sqrt (10)}{3}$}.
