To solve this equation, we need to simplify and combine like terms:

(7x - 35) * 2x - (7x - 35) * 50 = 0

First, let's distribute the terms inside the parentheses:

14x^2 - 70x - 350x + 1750 - 350x + 1750 = 0

Simplifying further:

14x^2 - 770x + 3500 = 0

Now, let's solve this quadratic equation. We can either factor it or use the quadratic formula. In this case, factoring is not possible, so we'll use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 14, b = -770, and c = 3500. Plugging these values into the quadratic formula:

x = (-(-770) ± √((-770)^2 - 4 * 14 * 3500)) / (2 * 14)

Simplifying:

x = (770 ± √(592900 - 196000)) / 28

x = (770 ± √(396900)) / 28

x = (770 ± 630) / 28

Now, we have two possible solutions:

x = (770 + 630) / 28 = 1400 / 28 = 50

x = (770 - 630) / 28 = 140 / 28 = 5

Therefore, the solutions to the equation are x = 50 and x = 5.