Let's solve each of these equations step by step:

975(y-361)=14625
Distribute the 975 on the left side:
975y - 975361 = 14625
975y - 352875 = 14625
Add 352875 to both sides:
975y = 368500
Divide by 975:
y = 378

(30142+z)-876=49
Add 876 to both sides:
30142 + z = 925
Subtract 30142 from both sides:
z = -29217

51815-:(p-975)=1205
Divide both sides by 1205:
51815 / (p-975) = 1205
Multiply both sides by (p-975):
51815 = 1205(p-975)
51815 = 1205p - 1174875
Add 1174875 to both sides:
1179690 = 1205p
Divide by 1205:
p = 980

13x+15x-24=60
Combine like terms:
28x - 24 = 60
Add 24 to both sides:
28x = 84
Divide by 28:
x = 3

18y-7y-10=12
Combine like terms:
11y - 10 = 12
Add 10 to both sides:
11y = 22
Divide by 11:
y = 2

Therefore, the solutions are: