Hello there!
We first want to start by setting the equation equal to 0.
We do this by adding/subtracting the costant to the right of the equal sign to both sides, like this:
2x^2+10x(+8) = (-8)(+8)
We now have 2x^2+10x+8=0
Now we find the GCF, which is 2 in this case because 2 goes into 2, 10, and 8. Now divide all terms by 2.
Now we have x^2+5x+4=0
To further factor we now need to take the last term (4) and the middle term (5) and find out what multiplies to be 4 and adds to be 5. The answer to this is 4 and 1.
Now we are left with (x+4) and (x+1). We have no leading coefficient to divide the x by, so now we set each new equation equal to 0 and solve by getting x by itself. It will look like this:
x+4=0, x+4(-4)=-4
x+1=0, x+1(-1)=-1
After factoring, your answers will be x=-4 and x=-1.
Hope this helps!