1. **State the problem:** Solve the equation $$52x - 120(5x) - 625 = 0$$ and understand how to factor the numbers easily. 2. **Rewrite the equation:** First, simplify the term $$-120(5x)$$ by multiplying: $$-120 \times 5x = -600x$$ So the equation becomes: $$52x - 600x - 625 = 0$$ 3. **Combine like terms:** $$52x - 600x = -548x$$ So the equation is: $$-548x - 625 = 0$$ 4. **Isolate the variable term:** Add 625 to both sides: $$-548x = 625$$ 5. **Solve for $$x$$:** Divide both sides by $$-548$$: $$x = \frac{625}{-548} = -\frac{625}{548}$$ 6. **Factoring tip:** To factor numbers easily, look for common factors or prime factorization. For example, 625 is $$5^4$$ and 548 can be factored as $$2 \times 2 \times 137$$. Since they share no common factors, the fraction is already in simplest form. **Final answer:** $$x = -\frac{625}{548}$$