Degearing and Regearing using M+M’s proposition 2 equation

Dear John Sir,

Kindly help me understand this question from Kaplan study text.

I am unable to understand how degearing and regearing is done in the below mentioned question. Although, I have mentioned the published answer as well but i am unable to understand how he get the ke of 10.8%.

I fail to understand the rearranging ……

Sir, please can you explain me in an easy steps. I will be very grateful.

Question:

Moondog Co is a company with a 20:80 debt:quality ratio. Using CAPM, its cost of equity has been calculated as 12%.
It is considering raising some debt finance to change its gearing ratio to 25:75 debt to equity. The expected return to debt holders is 4% per annum, and the rate of corporate tax is 30%

REQUIRED

Calculate the theoretical cost of equity in Moondog Co after the refinancing.

ANSWER
Using M+M’s proposition 2 equation, we can degear the existing ke and then regear it to the new gearing level

DEGEARING

Ke=kei+(1-T)(kei-kd)(Vd/Ve)
12%=kei+(1-0.30)(kei-4%)(20/80)

Rearranging carefully gives ke=10.8%

NOW REGEARING
Ke=10.8%+(1-0.30)(10.8%-4%)(25/75)
Ke=12.4%