First, distribute the terms in the first parentheses:

(2x - 9)(x + 6) = 2x^2 + 12x - 9x - 54 = 2x^2 + 3x - 54

Now, distribute the second term:

2x^2 + 3x - 54 - x(x + 6) = 2x^2 + 3x - 54 - x^2 - 6x = x^2 - 3x - 54

Now, set the equation equal to 0:

x^2 - 3x - 54 = 0

This is a quadratic equation, to solve for x, we can factor or use the quadratic formula:

(x - 9)(x + 6) = 0

Now, set each factor equal to 0:

x - 9 = 0 or x + 6 = 0

x = 9 or x = -6

Therefore, the solutions are x = 9 and x = -6.