Let's first simplify the left side of the equation by using the distributive property:

5(9t-3(2t-4)) + 12 = 4(t+29)
45t - 15(2t-4) + 12 = 4t + 116
45t - 30t + 60 + 12 = 4t + 116
15t + 72 = 4t + 116

Next, let's combine like terms by subtracting 4t from both sides and subtracting 72 from both sides:

15t - 4t = 116 - 72
11t = 44

Finally, divide both sides by 11 to solve for t:

11t/11 = 44/11
t = 4

Therefore, the solution to the equation is t = 4.