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2\left(x^{2}z+6xz+5z\right)
Factor out 2.
z\left(x^{2}+6x+5\right)
Consider x^{2}z+6xz+5z. Factor out z.
a+b=6 ab=1\times 5=5
Consider x^{2}+6x+5. Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx+5. To find a and b, set up a system to be solved.
a=1 b=5
Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. The only such pair is the system solution.
\left(x^{2}+x\right)+\left(5x+5\right)
Rewrite x^{2}+6x+5 as \left(x^{2}+x\right)+\left(5x+5\right).
x\left(x+1\right)+5\left(x+1\right)
Factor out x in the first and 5 in the second group.
\left(x+1\right)\left(x+5\right)
Factor out common term x+1 by using distributive property.
2z\left(x+1\right)\left(x+5\right)
Rewrite the complete factored expression.