$$\frac { 6 x + 7 } { 3 x + 2 } = \frac { 4 x + 5 } { 2 x + 3 }$$
$x = -\frac{11}{9} = -1\frac{2}{9} \approx -1.222222222$
$$\left(2x+3\right)\left(6x+7\right)=\left(3x+2\right)\left(4x+5\right)$$
$$12x^{2}+32x+21=\left(3x+2\right)\left(4x+5\right)$$
$$12x^{2}+32x+21=12x^{2}+23x+10$$
$$12x^{2}+32x+21-12x^{2}=23x+10$$
$$32x+21=23x+10$$
$$32x+21-23x=10$$
$$9x+21=10$$
$$9x=10-21$$
$$9x=-11$$
$$x=\frac{-11}{9}$$
$$x=-\frac{11}{9}$$
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