Let's first simplify the expression step by step:

(7-6c)(6c+7c) = (7-6c)(13c) = 7(13c) - 6c(13c) = 91c - 78c^2

-9c(2-4c) = -9c(2) - (-9c)(4c) = -18c + 36c^2

Putting it all together:

(7-6c)(6c+7c) - 9c(2-4c) - 49 = 91c - 78c^2 - 18c + 36c^2 - 49

Combining like terms:

91c - 78c^2 - 18c + 36c^2 - 49
= 91c - 18c - 78c^2 + 36c^2 - 49
= 73c - 42c^2 - 49

Therefore, the simplified expression is 73c - 42c^2 - 49.