What will be the solution set of 2x^2-6x=4x-12

The answer options in my book are:
{2, 1}
{2, 6}
{2, 3}
{ }

Now I'm confused because there is only one variable here, "x", so why two values in the solution set?

2x^2-6x = 4x-12

Subtract 4x from both sides:
2x^2-6x-4x = 4x-12-4x
2x^2-10x = -12

Add 12 to both sides:
2x^2-10x+12 = -12+12
2x^2-10x+12 = 0

Factor out 2 from the left side:
2(x^2-5x+6) = 0

Divide both sides by 2:
2(x^2-5x+6)/2 = 0/2
x^2-5x+6 = 0

Factor the trinomial on the left side:
(x-3)(x-2) = 0

Set each factor equal to 0 and solve:
Either x-3=0 or x-2=0.
Therefore x=3 or x=2.

Answer: x = {2,3}

2x^2-6x=4x-12
x^2-3x=2x-6
x^2-5x+6 = 0
(x-3)(x-2) = 0
x = 2 or 3
{2,3}
The number of solutions = highest power of x in the equation
Here we have x^2 so 2 solutions

Check with other answers i am not a mathlete.
{2,3}

2x^2-6x=4x-12
2x^2-6x-4x+12=0
2x^2-10x+12=0
(2x-4)(x-3)
x=4/2 x=3
x=2 x=3

Check
2(2)^2-6(2)=4(2)-12
8-12=8-12
-4=-4

2(3)^2-6(3)=4(3)-12
18-18=12-12
0=0

What's the last one? I just guess haha.

ask ur teacher on monday