The complex number $z = c$ is a solution to the equation $f(z) = 0$ (also called a zero or root of $f(z)$) if and only if $(z-c)$ is a factor of $f(z)$. The proof of this statement follows easily by adapting the Euclidean algorithm which concerns finding the greatest common divisor of integers to finding the greatest common divisor of functions. A proof of this statement would be easy enough that I could add it to the post if you like.
At any rate, use this idea and try to find a root to the equation $z^4 +2z^3 + 6z -9 = 0$. Finding a root then gives a factor, and reduces the degree of the polynomial you want to factor by $1$.
Now there are many ways to find the zeroes of $f(z)$. In the simplest cases, you can simply guess and check for solutions. The obvious candidates to check for zeroes are $z = 1, z = -1, z = 2, z= -2$, etc. Note that $z = 0$ is a zero if and only if $f(z)$ has no constant term. One of the more useful tests for finding roots of polynomials is the Rational Root Test. Other known methods for finding zeroes of polynomials include completing the square (for quadratic functions), using the cubic formula, or using the quartic formula, though the cubic and quartic formulae are a bit unwieldy in practice.