(x-11)(x+12)+120=2x

Let's solve this equation step by step:

1. Expand the left side of the equation using the distributive property:

(x-11)(x+12) + 120 = 2x (x^2 + x(-11) + x(12) + (-11)(12)) + 120 = 2x (x^2 - 11x + 12x - 132) + 120 = 2x x^2 + x - 12x - 132 + 120 = 2x x^2 - 11x - 12 + 120 = 2x x^2 - 11x + 108 = 2x

2. Move all terms to one side to create a quadratic equation:

x^2 - 11x + 108 - 2x = 0 x^2 - 13x + 108 = 0

3. Factorize the quadratic equation:

(x - 9)(x - 12) = 0

4. Use the zero product property to find the values of x:

x - 9 = 0 or x - 12 = 0 x = 9 x = 12

Therefore, the solutions to the equation are x = 9 and x = 12.