Block[{a, t, p, q, m, r},
Solve[{0.` + 18 b^2 - 20 a b^2 + 4 b^2 m - 8 a^2 b^2 m + 36 b n -
20 a b n - 2 b m n - 8.` a b m^2 n + 15 n^2 - 6 m n^2 -
2.` m^3 n^2 - 18 b p + 20 a b p - 4 b m p + 8 a b m p - 12 n p +
6 m n p + 4 m^2 n p + 6 b q - 4 b m q + 8 a b m q - 4 m n q +
4 m^2 n q - 6 p q + (124 m p q)/19 - 10 b r - 8.` a b m r -
10 n r - 4.` m^2 n r + 10 p r + 4 m p r + 4 m q r - 2.` m r^2 -
2 b t - 2 n t + 2 p t == 0,
0.` + 6 b^2 - 6 a b^2 - 8 a^3 b^2 + 18 b n - 2 a b n - 5 b m n -
8.` a^2 b m n + 9 n^2 + 4 a n^2 - 5 m n^2 - 2.` a m^2 n^2 -
6 b p + 6 a b p + 8 a^2 b p - 6 n p - 4 a n p + 5 m n p +
4 a m n p + 6 b q - 4 a b q + 8 a^2 b q - 4 a n q + 4 a m n q -
6 p q + (124 a p q)/19 - 5 b r - 8.` a^2 b r - 5 n r -
4.` a m n r + 5 p r + 4 a p r + 4 a q r - 2.` a r^2 - b t - n t +
p t == 0}, {n, b}]]

过于复杂的符号系数是会严重拖慢符号计算的，详见这帖：
http://mathematica.stackexchange.com/q/109733/1871
所以，使用那个帖里提及的程序包：
eqn = {0 + 18 b^2 - 20 a b^2 + 4 b^2 m - 8 a^2 b^2 m + 36 b n - 20 a b n - 2 b m n -
8 a b m^2 n + 15 n^2 - 6 m n^2 - 2 m^3 n^2 - 18 b p + 20 a b p - 4 b m p +
8 a b m p - 12 n p + 6 m n p + 4 m^2 n p + 6 b q - 4 b m q + 8 a b m q - 4 m n q +
4 m^2 n q - 6 p q + (124 m p q)/19 - 10 b r - 8 a b m r - 10 n r - 4 m^2 n r +
10 p r + 4 m p r + 4 m q r - 2 m r^2 - 2 b t - 2 n t + 2 p t == 0,
0 + 6 b^2 - 6 a b^2 - 8 a^3 b^2 + 18 b n - 2 a b n - 5 b m n - 8 a^2 b m n + 9 n^2 +
4 a n^2 - 5 m n^2 - 2 a m^2 n^2 - 6 b p + 6 a b p + 8 a^2 b p - 6 n p - 4 a n p +
5 m n p + 4 a m n p + 6 b q - 4 a b q + 8 a^2 b q - 4 a n q + 4 a m n q -
6 p q + (124 a p q)/19 - 5 b r - 8 a^2 b r - 5 n r - 4 a m n r + 5 p r + 4 a p r +
4 a q r - 2 a r^2 - b t - n t + p t == 0};
{neweqn, rule} =
Block[{a, t, p, q, m, r}, (*注意这个程序包要到上面那帖里去下载！*)
GroupConstants[Collect[eqn, {n, b}], {n, b}]]; // AbsoluteTiming
(* {0.003002, Null} *)
test = Solve[neweqn, {n, b}]; // AbsoluteTiming
(* {55.110359, Null} *)
sol = test /. rule;