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