The below information provided and I also have the results. I'm looking to be explained the math part. I'm not understanding how the math was done to solve for "X".

Copper Pipe Inc. is trying to estimate its optimal capital structure. Right now, Copper Pipe has a capital structure that consists of 20 percent debt and 80 percent equity, based on market values. (Its D/S ratio is 0.25.) The risk-free rate is 6 percent and the market risk premium, rM - rRF, is 5 percent. Currently the company's cost of equity, which is based on the CAPM, is 12 percent and its tax rate is 40 percent. What would be Copper Pipe Inc's estimated cost of equity if it were to change its capital structure to 50 percent debt and 50 percent equity?

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Facts

k_s = 12%

D/E = 0.25

k_RF = 6%

RP_M = 5%

T = 40%

Find the firm's current levered beta using the CAPM:

K_s = k_rf + RP _m(x)

12% = 6% + 5%(x)

X = 1.2

Find the firm's unlevered beta using the Hamada equation:

X = b_u[1 + (1 - T)(D/E)]

1.2 = b_u[1 + (0.6)(0.25)]

1.2 = 1.15b_u

1.0435 = b_u

Find the new levered beta given the new capital structure using the Hamada equation

X = bu[1 +(1- T)(D/E)]

X = 1.0435[1 + (0.6)(1)]

X = 1.6696

Find the firm's new cost of equity given its new beta and CAPM

K_s = k_RF + RP_M(x)

K_s = 6% + 5%(1.6696)

K_s = 14.35%