1. **State the problem:** Solve for $x$ in the equation $3x - 7(-4x + 5) = 6$. 2. **Apply the distributive property:** Multiply $-7$ by each term inside the parentheses: $$3x - 7(-4x) - 7(5) = 6$$ which simplifies to $$3x + 28x - 35 = 6$$ 3. **Combine like terms:** $$3x + 28x = 31x$$ So the equation becomes $$31x - 35 = 6$$ 4. **Isolate the variable term:** Add $35$ to both sides: $$31x = 6 + 35$$ $$31x = 41$$ 5. **Solve for $x$:** Divide both sides by $31$: $$x = \frac{41}{31}$$ 6. **Final answer:** $$x = \frac{41}{31}$$