Solve the equation to find $x$. \[ \begin{aligned} 5(2 x+4) & =8(x-3) \\ x & =1 \end{aligned} \]

Step 1 ：Distribute the 5 on the left side of the equation and the 8 on the right side of the equation to get \(10x + 20 = 8x - 24\).

Step 2 ：Subtract 8x from both sides of the equation to get \(2x + 20 = -24\).

Step 3 ：Subtract 20 from both sides of the equation to get \(2x = -44\).

Step 4 ：Divide both sides of the equation by 2 to solve for x, which gives \(x = -22\).

Step 5 ：Substitute \(x = -22\) back into the original equation to verify that both sides of the equation are equal.

Step 6 ：Final Answer: The solution to the equation is \(\boxed{-22}\).