Okay, first let's factor 5a.
Because we know that 4+3 = 7, and that -4*-3 = 12, we also know that x^2 - 7x + 12 can be factored into:
(x - 4)(x-3) = 0
Knowing that only one has to equal zero, we know that x = [4, 3]
Now, onto 5b.
2z^2 + 9z + 3 = 0
It doesn't seem like this equation can be factored, so 5b would be no solution.
Now, onto 6a.
x^2 - 18x = -72
We add 81 to both sides:
x^2 - 18x + 81 = 9
(x-9)^2 = 9
Square root both:
(x-9) = 3
x = 12
Now, for the final question:
x^2 + 2x + 8 = 0
Move 8 to the other side:
x^2 + 2x = -8
Subtract 1 from both sides:
x^2 + 2x - 1 = -9
Hmm, it doesn't seem like this would work. This answer is also no solution.