1. **State the problem:** Solve the equation $7x + 12 = (x + 3)(x + 4)$ and understand how the factors 3 and 4 appear. 2. **Expand the right side:** Use the distributive property (FOIL) to expand $(x + 3)(x + 4)$: $$ (x + 3)(x + 4) = x \cdot x + x \cdot 4 + 3 \cdot x + 3 \cdot 4 = x^2 + 4x + 3x + 12 = x^2 + 7x + 12 $$ 3. **Rewrite the equation:** Now the equation is $$ 7x + 12 = x^2 + 7x + 12 $$ 4. **Bring all terms to one side:** Subtract $7x + 12$ from both sides: $$ 7x + 12 - 7x - 12 = x^2 + 7x + 12 - 7x - 12 $$ $$ 0 = x^2 $$ 5. **Simplify:** This simplifies to $$ x^2 = 0 $$ 6. **Solve for $x$:** Taking the square root of both sides, $$ x = 0 $$ 7. **Explanation of factors 3 and 4:** The numbers 3 and 4 come from the original factorization of the quadratic expression on the right side. The expression $x^2 + 7x + 12$ factors into $(x + 3)(x + 4)$ because 3 and 4 are two numbers that multiply to 12 (the constant term) and add to 7 (the coefficient of $x$). **Final answer:** $$ x = 0 $$