1. **State the problem:** Solve the equation $ (x + 5)(x + 1) + 2(x - 4)(x + 3) = 3x(x + 8) $.\n\n2. **Expand each product:**\n\n$ (x + 5)(x + 1) = x^2 + x + 5x + 5 = x^2 + 6x + 5 $\n$ (x - 4)(x + 3) = x^2 + 3x - 4x - 12 = x^2 - x - 12 $\n\n3. **Substitute expansions back into the equation:**\n\n$ x^2 + 6x + 5 + 2(x^2 - x - 12) = 3x(x + 8) $\n\n4. **Distribute the 2:**\n\n$ x^2 + 6x + 5 + 2x^2 - 2x - 24 = 3x^2 + 24x $\n\n5. **Combine like terms on the left:**\n\n$ (x^2 + 2x^2) + (6x - 2x) + (5 - 24) = 3x^2 + 24x $\n$ 3x^2 + 4x - 19 = 3x^2 + 24x $\n\n6. **Bring all terms to one side:**\n\n$ 3x^2 + 4x - 19 - 3x^2 - 24x = 0 $\n\n7. **Simplify:**\n\n$ \cancel{3x^2} + 4x - 19 - \cancel{3x^2} - 24x = 0 $\n$ 4x - 24x - 19 = 0 $\n$ -20x - 19 = 0 $\n\n8. **Solve for $x$:**\n\n$ -20x = 19 $\n$ x = \frac{19}{-20} = -\frac{19}{20} $\n\n**Final answer:** $ x = -\frac{19}{20} $