To solve the equation \( x^2 - 36 = 0 \) using factoring, we recognize that it can be expressed as a difference of squares. The difference of squares formula is given by:
\[ a^2 - b^2 = (a - b)(a + b) \]
In our case, we can identify \( a^2 = x^2 \) and \( b^2 = 36 \) (which means \( b = 6 \)). Thus, we can factor the equation as follows:
\[ x^2 - 36 = (x - 6)(x + 6) \]
Next, we set the factored expression equal to zero:
\[ (x - 6)(x + 6) = 0 \]
Using the zero product property, we can set each factor equal to zero:
- \( x - 6 = 0 \)
- \( x + 6 = 0 \)
Solving these equations gives us:
- \( x = 6 \)
- \( x = -6 \)
Therefore, the solutions to the equation \( x^2 - 36 = 0 \) are:
\[ \boxed{6} \quad \text{and} \quad \boxed{-6} \]