$$\frac{3x+5}{4x+2}=\frac{3x+4}{4x+7}$$
$x = -\frac{27}{19} = -1\frac{8}{19} \approx -1.421052632$
$$\left(4x+7\right)\left(3x+5\right)=\left(4x+2\right)\left(3x+4\right)$$
$$12x^{2}+41x+35=\left(4x+2\right)\left(3x+4\right)$$
$$12x^{2}+41x+35=12x^{2}+22x+8$$
$$12x^{2}+41x+35-12x^{2}=22x+8$$
$$41x+35=22x+8$$
$$41x+35-22x=8$$
$$19x+35=8$$
$$19x=8-35$$
$$19x=-27$$
$$x=\frac{-27}{19}$$
$$x=-\frac{27}{19}$$
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