whats the best way to check answers?

If you do algebra, the best way is to substitue all the numbers you find back in.

5x+7=20

20-7=15

5x=15

x=3?

3x5+7=20?

15+7=22 not 20 so x=/=3 so somewhere i went wrong.

Sometimes, doing a question a number of times can help check for errors. Say i had a binomial expantion. I would do it at least twice to make sure all the answers I got were the same.

You can also rearrange an answer to see if it still works and also do some question backwards to see if you get the same start.

34x29-12=972?

972 +12 = 984

984/29=33.586

Somewhere i went wrong.

Dont forget to reverse bidmas/bodmas/pidmas or whatever you call it when reversing a calculation.

If its done on a calculator, you can input the question in a number of times to make sure you didn't press a wrong button.

umm... by using a calculator

This is a very broad question. 

There are a lot of sanity tests in mathematics. 

If you multiply a lot of natural numbers, where one of the factors is even, the product must be even. 

If you multiply a lot of natural numbers, where one of the factors is divisible by three, the product must be divisible by three, and hence, the digit sum divisible by three. 

Be careful with units. "Newton" is force, not energy.