5/12(c-3)-1/6(2c-7)=2

To solve the equation \(\frac{5}{12}(c - 3) - \frac{1}{6}(2c - 7) = 2\), we will start by eliminating the fractions to make the equation easier to work with.

First, let's find a common denominator for the fractions. The least common multiple of 12 and 6 is 12. We can multiply the entire equation by 12 to eliminate the denominators:

\[ 12 \left( \frac{5}{12}(c - 3) \right) - 12 \left( \frac{1}{6}(2c - 7) \right) = 12 \cdot 2 \]

This simplifies to:

\[ 5(c - 3) - 2(2c - 7) = 24 \]

Now, distribute on the left side:

\[ 5c - 15 - 4c + 14 = 24 \]

Combine like terms:

\[ (5c - 4c) + (-15 + 14) = 24 \]

This simplifies to:

\[ c - 1 = 24 \]

Now, add 1 to both sides to solve for \(c\):

\[ c = 25 \]

Thus, the solution to the equation is:

\[ \boxed{25} \]