f(x) = -9x^2 - 7x + 12
g(x) = 3x^2 - 4x - 15
f(x) - g(x) =
= (-9x^2 - 7x + 12) - (3x^2 - 4x - 15)
The first set of parentheses is unnecessary, so we just drop it.
The second set of parentheses follows a negative sign, so it is as if a -1 multiplies the parentheses. To distribute the -1, you change each sign inside the parentheses.
= -9x^2 - 7x + 12 - 3x^2 + 4x + 15
Now, combine like terms.
= -12x^2 - 3x + 27