You combine like terms so that is -2z and +7z. Which equals 5. So now the equation is 5z + 3 = -12. You will then subtract three from -12 this is because when it's a positive you subtract, when it's a negative you add, when it's multiplication you divide and when it's division you multiply it to the the number after the equal sign which is -12. So now this makes it -15. Now the equation is 5z = -15. The final step is to divide. -15 divided by 5z equals -3. To check your answer you can plug -3 into the z's doing this will make the equation 6 + 3 -21 = -12. And everything should check out.
