How do I solve this?

First, solve for -2^3, which is -2 * -2 * -2, or -8. Then you can combine the -8 with the 7 to get -1. This leaves you with: (-2) = -x^2 - 1.
Next, you can add 2 to both sides, giving you: 0 = -x^2 + 1. Add x^2 to both sides to get x^2 = 1.
Finally, square root both sides, to get: x = +/- 1.