1. Let's start by stating the problem: factoring an equation means rewriting it as a product of simpler expressions. 2. The most common form to factor is a quadratic equation $ax^2 + bx + c$. 3. The formula to factor such an equation is to find two numbers that multiply to $ac$ and add to $b$. 4. For example, to factor $x^2 + 5x + 6$, find two numbers that multiply to $6$ and add to $5$; these are $2$ and $3$. 5. Rewrite the middle term using these numbers: $x^2 + 2x + 3x + 6$. 6. Group terms: $(x^2 + 2x) + (3x + 6)$. 7. Factor each group: $x(x + 2) + 3(x + 2)$. 8. Factor out the common binomial: $(x + 3)(x + 2)$. 9. So, $x^2 + 5x + 6$ factors to $(x + 3)(x + 2)$. 10. This method works for many quadratic equations and is called factoring by grouping. 11. For other types of equations, different methods like factoring out the greatest common factor or using special formulas (difference of squares, perfect square trinomials) apply. 12. Always check your factors by expanding to verify correctness.