(х+3)^-2(х+3)-8=0

To solve the equation \((x+3)^{-2}(x+3) - 8 = 0\), we can first simplify the expression.

1. Simplify the term \((x+3)^{-2}(x+3)\): \[ (x+3)^{-2}(x+3) = (x+3)^{-1} = \frac{1}{x+3} \]

2. So, the equation becomes: \[ \frac{1}{x+3} - 8 = 0 \]

3. To isolate the fractional term, we can add 8 to both sides: \[ \frac{1}{x+3} = 8 \]

4. Next, we can cross-multiply to solve for \(x\): \[ 1 = 8(x+3) \]

5. Expand the right side: \[ 1 = 8x + 24 \]

6. Subtract 24 from both sides: \[ 1 - 24 = 8x \] \[ -23 = 8x \]

7. Divide both sides by 8 to solve for \(x\): \[ x = -\frac{23}{8} \]

Thus, the solution to the equation is: \[ \boxed{-\frac{23}{8}} \]