2x to the second power minus 11x plus 12 equals 0?

2x^2 - 11x + 12 = 0
2x^2 - 3x - 8x + 12 = 0
(2x^2 - 3x) - (8x - 12) = 0
x(2x - 3) - 4(2x - 3) = 0
(2x - 3)(x - 4) = 0

2x - 3 = 0
2x = 3
x = 3/2 (1.5)

x - 4 = 0
x = 4

∴ x = 3/2 (1.5), 4

x^2-x-110=0 => ( x+10)(x-11)=0 => x=11 , x= -10

2 x ² - 11 x + 12 = 0

( 2 x - 3 ) ( x - 4 ) = 0

x = 3/2 , x = 4

Simple Quadratic equation.

x=4 or 3/2

Factor and use the zero product rule
There are several ways to factor 2x^2 - 11x + 12. I'll do it by grouping

split the -11x into -8x and -3x (because they add to -11 and multiply to 24 (2*12))

2x^2 - 8x - 3x + 12 = 0
group the first and last terms
(2x^2 - 8x)+(-3x +12)=0
factor each ( )

2x(x - 4) -3(x - 4)=0

put together (factor out the common factor of (x-4)

(2x - 3)(x - 4) = 0
split into 2 equations and solve, giving you x = 3/2 and x = 4.

2x^2 - 11x + 12 = 0

=> (2x-3)(x-4) = 0

=> x = 3/2 or x = 4

There are a couple of ways to solve this problem. One would be to try to guess factors and divide out, for example:

guessing (x-1) might be a factor,

2x^2 - 11x + 12 / (x-1) =

2x...2x^2 - 11x + 12
..-...2x^2 - 2x
......................=
..............-9x + 12
-9.....-.....-9x + 9
.......................3

So (x-1) does not divide evenly (leaves a remainder of 3). You can try other factors.

The other approach is to use the quadratic equation (look it up in your text book).