$$(\frac{2t-3}{5})+(\frac{t-3}{7})=(\frac{4t+1}{7})$$
$t=-41$
$$7\left(2t-3\right)+5\left(t-3\right)=5\left(4t+1\right)$$
$$14t-21+5\left(t-3\right)=5\left(4t+1\right)$$
$$14t-21+5t-15=5\left(4t+1\right)$$
$$19t-21-15=5\left(4t+1\right)$$
$$19t-36=5\left(4t+1\right)$$
$$19t-36=20t+5$$
$$19t-36-20t=5$$
$$-t-36=5$$
$$-t=5+36$$
$$-t=41$$
$$t=-41$$
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