Help Me Solve Missing Step in Characteristic Equation

[Maxwell]

I'm not sure why I can't see what step is occurring here, but I could use some help:

$$G(s) = \frac {30}/{(s^2 + 6s +20)}$$

$$H(s) = \frac {k} /{s+8}$$

Characterisic equation: $$1+ G(s)H(s)$$

So,

$$1 + \frac ({30k} /{(s^2+6s+20)(s+8))} = 0$$

Then, the step I'm not sure about:

$$(s^2+6s+20)(s+8) + 30k = 0$$

How do I get to that step? For some reason I can't see the simple algebra that is used.

 

[dav2008]

I'm not sure why I can't see what step is occurring here, but I could use some help:

$$G(s) = \frac {30}{s^2 + 6s +20}$$

$$H(s) = \frac {k} {s+8}$$

Characterisic equation: $$1+ G(s)H(s)$$

So,

$$1 + \frac{30k} {(s^2+6s+20)(s+8)} = 0$$

Then, the step I'm not sure about:

$$(s^2+6s+20)(s+8) + 30k = 0$$

How do I get to that step? For some reason I can't see the simple algebra that is used.

Is this what you meant to write?

It looks like they just multiplied both sides by $$(s^2+6s+20)(s+8)$$

 

[Cyrus]

Doing a little controls theory are we? Yep, just mutliply both sides by that.

 

[Maxwell]

Yup, control theory. I don't know why I couldn't see that step, I think it's time to take a break. :rofl:

Thanks guys.