$$\frac{3t+1}{16}-\frac{2t-3}{7}=\frac{t+3}{8}+\frac{3t-1}{14}$$
$t=\frac{3}{7}\approx 0.428571429$
$$7\left(3t+1\right)-16\left(2t-3\right)=14\left(t+3\right)+8\left(3t-1\right)$$
$$21t+7-16\left(2t-3\right)=14\left(t+3\right)+8\left(3t-1\right)$$
$$21t+7-32t+48=14\left(t+3\right)+8\left(3t-1\right)$$
$$-11t+7+48=14\left(t+3\right)+8\left(3t-1\right)$$
$$-11t+55=14\left(t+3\right)+8\left(3t-1\right)$$
$$-11t+55=14t+42+8\left(3t-1\right)$$
$$-11t+55=14t+42+24t-8$$
$$-11t+55=38t+42-8$$
$$-11t+55=38t+34$$
$$-11t+55-38t=34$$
$$-49t+55=34$$
$$-49t=34-55$$
$$-49t=-21$$
$$t=\frac{-21}{-49}$$
$$t=\frac{3}{7}$$
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