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Factoring quadratic equations is a fundamental algebraic skill required to solve equations of the form \( ax^2+bx+c=0 \). It involves finding two binomials that multiply together to give the original quadratic equation. To begin factoring a quadratic, you first check if there is a greatest common factor among the terms. If so, factor it out. Then, if the quadratic is simple and has the form \( x^2+bx+c \), try finding two numbers that multiply to 'c' and add the middle coefficient 'b'.

When an equation cannot be factored easily, other methods like the square root method or completing the square are used. In the context of our exercise \( (b+5)^2=16 \), factoring isn’t needed directly as the quadratic is already in a squared binomial form, which leads us to apply the square root method for this particular problem.

The square root method offers a straightforward way to solve quadratic equations that are in the form of a perfect square, similar to our example \( (b+5)^2=16 \). This method involves taking the square root of both sides of the equation to eliminate the exponent on the squared term. In doing so, remember to include both the positive and negative square roots, since both \( (\pm a)^2 = a^2 \).

After simplifying, you should have an equation without the squared term, making it easier to isolate the variable. The key steps include rewriting the equation to get the square alone on one side, taking the square root of both sides, and then solving the resulting linear equations. Using this method is typically efficient for equations that readily form perfect squares, but it may not be suitable for all types of quadratic equations.

Isolating the variable is the final step in solving equations, including quadratics. This technique involves manipulating the equation in such a way that the unknown variable stands alone on one side, while all other terms are on the opposite side. This often requires you to perform operations like addition, subtraction, multiplication, or division across the equation.

In our exercise, we isolate 'b' by subtracting 5 from both sides of the split equations \( b+5=4 \) and \( b+5=-4 \). This step arises after applying the square root method, leading to two possible solutions for 'b'. Always check your solutions by substituting them back into the original equation to verify that they indeed resolve the equation correctly. The isolation of the variable is a universal step in solving for unknowns and crucial for finding the exact values that satisfy the equation.