If you split it into sections it should be easier than combining it into one.

If you have $F_1$ , $F_2$, $F_3$ as the tensions of the strings

$$
F_{1x} = F_{2x}
$$
$$
F_{2x} = F_{3x}
$$
$$
F_{1y} + F_{2y} = 12g
$$
$$
F_{2y} + 7g = F_{3y}
$$

Then you can use trigonometry and then eliminate.