Simplify 5t + (t - 3) - [(7t + 5) - (8 - 3t)].= -4t but why is that the right answer?

Simplify the following:
5 t + (t - 3) - ((7 t + 5) - (8 - 3 t))

-(8 - 3 t) = 3 t - 8:
5 t + t - 3 - (3 t - 8 + 7 t + 5)

Grouping like terms, 7 t + 3 t - 8 + 5 = (7 t + 3 t) + (5 - 8):
5 t + t - 3 - ((7 t + 3 t) + (5 - 8))

7 t + 3 t = 10 t:
5 t + t - 3 - (10 t + (5 - 8))

5 - 8 = -3:
5 t + t - 3 - (10 t + -3)

Grouping like terms, 5 t + t - 3 - (10 t - 3) = -(10 t - 3) + (5 t + t) - 3:
-(10 t - 3) + (5 t + t) - 3

5 t + t = 6 t:
-(10 t - 3) + 6 t - 3

-(10 t - 3) = 3 - 10 t:
3 - 10 t + 6 t - 3

Grouping like terms, 3 - 10 t + 6 t - 3 = (3 - 3) + (6 t - 10 t):
(3 - 3) + (6 t - 10 t)

6 t - 10 t = -4 t:
-4 t + (3 - 3)

3 - 3 = 0:
-4 t

Agc and bgd are vertical angles