Verified answer

move 8 across the other side and take out a as a common factor

a(a^2 + 6a +12) = -8

therefore, a=8, or (a^2 + 6a +12)=8

use the quadratic equation to find a in second value

a^3+6a^2+12a+8=(a+2)^3 = 0 ------> a = -2

You can use either synthetic division, or factor out the equation which will give you (a+2)(a+2)(a+2) = 0.

Solving for a, you will get a= -2.