(5x^4+6x^3-43)+(6x^5-x^2+12x+12) how do you solve this?

There is no solution without an equal sign.

First you rewrite the statement to improve readability.

(5x^4 + 6x^3 - 43) + (6x^5 - x^2 + 12x + 12)

Minus 43 and plus 12 are the only ones that can be added. Rewrite in order of descending powers.

6x^5 + 5x^4 + 6x^3 - x^2 + 12x - 31

This is called "gathering terms".