Solve the equation. \( \frac{x+6}{5}-\frac{x+3}{2}=0 \)

To solve the equation \( \frac{x+6}{5}-\frac{x+3}{2}=0 \), let's find a common denominator, which is 10. We can rewrite the equation: \[ \frac{2(x+6)}{10} - \frac{5(x+3)}{10} = 0 \] Now, we can combine the fractions: \[ \frac{2(x+6) - 5(x+3)}{10} = 0 \] This leads us to the numerator: \[ 2(x+6) - 5(x+3) = 0 \] Expanding both parts gives: \[ 2x + 12 - 5x - 15 = 0 \] Combining like terms results in: \[ -3x - 3 = 0 \] To isolate \( x \), we can rearrange: \[ -3x = 3 \quad \Rightarrow \quad x = -1 \] Thus, the solution to the equation is \( x = -1 \).