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\left(a+m-3-x\right)\left(a+m+3+x\right)
Rewrite 2am-x^{2}-9+a^{2}+m^{2}-6x as \left(a+m\right)^{2}-\left(3+x\right)^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).
\left(-x+a+m-3\right)\left(x+a+m+3\right)
Reorder the terms.