Question

If the solutions to an equation are 2 and –3, which of the following could be the equation?

Answer 1

The solutions are 2 and -3 which means a factored equation would be (x-2)(x+3)
simplify it and you get A

Answer 2

The solutions are 2 and -3 so we can write our equation as:

$a\cdot(x-2)(x+3)=0\\\\a\cdot(x^2-2x+3x-6)=0\\\\a\cdot(x^2+x-6)=0\\\\ax^2+ax-a\cdot6=0$

and for a = 2 there will be:

$ax^2+ax-a\cdot6=0\\\\ 2x^2+2x-2\cdot6=0\\\\ 2x^2+2x-12=0\quad|+12\\\\\boxed{2x^2+2x=12}$

Answer D.