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Factoring quadratics is a fundamental method used to solve quadratic equations. When you turn a quadratic equation into a product of simpler expressions, you can solve it more easily. For example, consider the equation from the exercise: oindent \(x^2 - 36 = 0 \).
This can be factored into: oindent \( (x - 6)(x + 6) = 0 \).
Here, we've turned a complex quadratic equation into two simple linear terms.
Factoring helps because if a product of two numbers equals zero, one (or both) of those numbers must be zero. That means we can set each factor equal to zero and solve the simpler equations.

Understanding what a quadratic equation is, helps in recognizing and solving them effectively. A quadratic equation is any equation that can be formulated as oindent \( ax^2 + bx + c = 0 \), where a, b, and c are constants, and a is not zero. In our example, the equation: < noindent \( x^2 - 36 = 0 \) takes the specific form of oindent \( ax^2 + bx + c \) with:
\[ a = 1, \ b = 0, \ c = -36 \].
It's important to rewrite the equation in this standard form so you can apply different solving methods like factoring, using the quadratic formula, or completing the square.
For this problem, factoring is the simplest approach. Still, other quadratics may need different methods if they can't be easily factored.

Once a quadratic equation is factored, you often end up with simpler linear equations. Solving these linear equations is the final step. From our factored form: oindent \( (x - 6)(x + 6) = 0 \),
we set each factor to zero: oindent \( x - 6 = 0 \) and oindent \( x + 6 = 0 \).
Solving these gives us the simple linear equations: \[ x = 6, \ x = -6 \].
Linear equations are straightforward because you perform arithmetic operations to isolate the variable. Here, you can directly see that x equals 6 or -6 by simply adding or subtracting 6.