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

To solve the equation (x-11)(x+12)+120=2x, we need to simplify the left side of the equation and then solve for x.

Expanding the left side of the equation: (x-11)(x+12) + 120 = 2x (x^2 + 12x - 11x - 132) + 120 = 2x (x^2 + x - 12) + 120 = 2x

Combining like terms: x^2 + x - 12 + 120 = 2x x^2 + x + 108 = 2x

Rearranging the equation: x^2 - x - 2x + 108 = 0 x^2 - 3x + 108 = 0

Now we have a quadratic equation. We can solve it by factoring or by using the quadratic formula.

To factor the quadratic equation, we need to find two numbers that multiply to 108 and add up to -3.

The numbers are -9 and -12: (x - 9)(x - 12) = 0

So, x - 9 = 0 or x - 12 = 0

Solving for x:

x - 9 = 0 x = 9

x - 12 = 0 x = 12

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