Solve the following equation by factoring. Write your answer in reduced fraction form, if necessary.
z^2+6z+8=0
To factor the quadratic equation z^2+6z+8=0, we need to find two numbers whose sum is 6 and whose product is 8. The numbers that satisfy this condition are 2 and 4.
Therefore, we can rewrite the equation as (z+2)(z+4) = 0.
Now, we set each factor equal to zero and solve for z:
z+2 = 0 => z = -2
z+4 = 0 => z = -4
Thus, the solutions to the equation z^2+6z+8=0 are z = -2 and z = -4.