Simplify the Expression: 25x+33y+6z-(14-(-12y)-3z)

First, let's address the expression in the innermost parentheses.

Let's remember that:

When we multiply a negative number by a negative number, the result will be positive.

Now we get:

$25x+33y+6z-(14+12y-3z)=$

Let's address the expression in parentheses and also remember the rule:

When we multiply a positive number by a negative number, the result will be negative.

We get:

$25x+33y+6z-14-12y+3z=$

Now let's combine the y coefficients:

$33y-12y=21y$

Now let's combine the z coefficients:

$6z+3z=9z$

And we get:

$25x+21y+9z-14$