"finding values that satisfy the equation" is just another way of asking you to find the zeroes of the equation. you can find the zeroes/values by factoring:
x² + 4x + 3 = 0 ... factor by trial and error, finding factors of 3 that add up to 4. try 3 and 1.
(x + 1)(x + 3) = 0 ... the next step is to set both of these factors to zero
x + 1 = 0 ... subtract 1 ... x = -1
x + 3 = 0 ... subtract 3 ... x = -3
so the values that satisfy this equation are -1 and -3.