Solve for the following variable(s):

3y - 8 + y - 12 = 2x - 20 + 6x - 10

To which I simplified it:
4y - 20 = 8x - 30

How do I simplify it further, and am I able to find both x and y?

Check your textbook...

Are they just asking you to re-arrange to get x all by itself, then to do the same and get y all by itself?

No, it just says to find the values of the variables. It is, however, having to do with angles, if that's any help.

Wait, I think I figured it out. Thanks for your replies!

To simplify the equation further, you can rearrange it to isolate either the variable 'y' or the variable 'x'. Let's isolate the variable 'y' in this case.

Starting with:
4y - 20 = 8x - 30

Add 20 to both sides of the equation to move the constant term to the right side:
4y = 8x - 30 + 20
4y = 8x - 10

Next, divide both sides of the equation by 4 to solve for 'y':
(4y)/4 = (8x - 10)/4
y = 2x - 2.5

So the simplified equation is y = 2x - 2.5.

From this equation, you can solve for 'y' in terms of 'x', but it cannot be used to find the exact values for both 'x' and 'y'. To find specific solutions, you will need additional information or another equation with variables 'x' and 'y'.