What are the values of x that satisfy the equation x ^2 + 4x+3=0

"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.