for the first one, you could use the quadratic formula. quadratic equations come with the form ax^2 + bx + c = 0, so we want to apply the quadratic formula: x = (-b +(or minus) squareroot(b^2-4ac) ) all over 2a
from 12b^2 - 192 ; a = 12, b = 0, c = -192 and then you plug into the equation then once you do it twice, both with the + sign and then the - sign you'll know how to factor the equation by setting (b - first root)(b - 2nd root) of course, if the roots are negative then you'd change the - sign to + and also, if it's all negative under the square root when using the quadratic formula, then you know you're using imaginary numbers.
q(q+4) = 0 the roots are q = 0 and q = -4. you can think of this as 2 equations on the left side, cover one of them and see what q equals. q(q+4) = 0, covering up q, you're left with q+4 = 0 and that's how you get q= -4 and etc.
(w-13)^2 = 16; you use PEMDAS
we have an exponent that we want to undo
so we take the exponent of (1/2) on both sides so we have
((w-13)^2)^(1/2) = 16(1/2)
then we have w-13 = 4
then we know w = 17
we know this is true because you plug 17 back in for w and you see 17-13 = 4 and squaring it, 4*4 = 16, hooray!