Hello, I would like to check how to get X (12.50) algebraically ,step by step from the following equation. Thanks a lot.

CIQ Inc. is a company that provides information services to financial service companies. The company currently has 150 million shares, trading at $ 10 a share, and $ 500 million in debt (book and market). The firm currently has a beta (levered) of 1.20 and a pre-tax cost of debt of 6%; the marginal tax rate is 40%; the risk free rate is 4% and the equity risk premium is 5%. The firm is considering borrowing $ 500 million and buying back stock; it believes that doing so will lower its cost of capital to 8%. (You can assume no growth in the savings in perpetuity)

1. assume that you do not know what the price per share will be on the stock buyback. How much would the price per share on the buyback have to be for the value per share on the remaining shares to remain unchanged at $10/share?

Let the price paid back be X

Number of shares bought back = 500/X

Premium paid = X-10

Value paid to buyback shares = (500/X) (X-10)

For the value per share on remaining shares to be unchanged

Value paid to buyback shares = $100.00

(500/X) (X-10) = 100

X =$12.50