Solve by factoring

a^2-6a+9=0

looks like a perfect square

(a - 3)^2 = 0
aa-3 = 0
a = 3

a^2-6a+9=0

To solve the given quadratic equation by factoring, we need to rewrite the equation in the form of "(expression) x (expression) = 0". In this case, the equation is:

a^2 - 6a + 9 = 0

Now, let's look for two binomials that we can multiply together to obtain this quadratic equation. The binomials will have the form:

(a - p)(a - q) = 0

To find the values of "p" and "q", we need to consider two factors: the leading coefficient of the quadratic term (which is 1 in this case) and the constant term (which is 9 in this case).

The constant term, 9, can only be factored as 3 x 3.

So, we can rewrite the equation as:

(a - 3)(a - 3) = 0

Since both binomials are the same, we can simplify it further:

(a - 3)^2 = 0

Now, we can apply the zero-product property, which states that if a product of factors is equal to zero, then at least one of the factors must be equal to zero. Therefore, we set each factor equal to zero and solve for "a":

(a - 3) = 0

By adding 3 to both sides, we obtain:

a = 3

Thus, the solution to the quadratic equation a^2 - 6a + 9 = 0 is a = 3.