#### Answer

$z=-4$

#### Work Step by Step

We start with the given equation: $-6z+1=13-3z$
We subtract $1$ from both sides of the equation, add $3z$ to both sides of the equation, and combine like terms: $$-6z+3z+1-1=13-1-3z+3z$$$$-3z=12$$
We divide by $-3$ on each side of the equation: $$\frac{-3z}{-3}=\frac{12}{-3}$$$$z=-4$$