Please help If x, y, and z are positive integers such that 6xyz+30xy+21xz+2yz+105x+10y+7z=812, find x+y+z.

Step-by-step explanation:

First we have to factor the equation:

The commom factor of first three terms and is . Note that

In order to have two equal factors add 35 both sides:

Let's factor

Now we have:

Now it is the interesting part: You have to figure out that 3 numbers multiplied by each other will result in 847.

We have

Let's try

I will stop right here. This is not true.

Let's try then

Now let's try

Now let's try

Note that in this case I didn't considered because it would not be an integer.

Therefore,