Answer
$x=-\dfrac{1}{5}$
Work Step by Step
By cross-multiplication, the solution to the given equation, $
\dfrac{2x+3}{3x-2}=\dfrac{4x+1}{6x+1}
,$ is
\begin{array}{l}
(2x+3)(6x+1)=(3x-2)(4x+1)
\\\\
12x^2+2x+18x+3=12x^2+3x-8x-2
\\\\
(12x^2-12x^2)+(2x+18x-3x+8x)=-2-3
\\\\
25x=-5
\\\\
x=-\dfrac{5}{25}
\\\\
x=-\dfrac{1}{5}
.\end{array}
