7(x-4)+3=3(2x-7)+x-8

To solve the equation \( 7(x-4) + 3 = 3(2x-7) + x - 8 \), we will first simplify both sides.

Starting with the left side:

\[ 7(x - 4) + 3 = 7x - 28 + 3 = 7x - 25 \]

Now simplify the right side:

\[ 3(2x - 7) + x - 8 = 6x - 21 + x - 8 = 6x - 21 - 8 = 6x - 29 \]

Now we have:

\[ 7x - 25 = 6x - 29 \]

Next, we will isolate \(x\). To do this, subtract \(6x\) from both sides:

\[ 7x - 6x - 25 = -29 \]

This simplifies to:

\[ x - 25 = -29 \]

Now, add \(25\) to both sides:

\[ x = -29 + 25 \]

Therefore:

\[ x = -4 \]

The solution to the equation is:

\[ \boxed{-4} \]