For this case we must find an equation, whose solutions are given by:
[tex]x = 2\\x = -3[/tex]
Or equivalently:
[tex](x-2) (x + 3) = 0[/tex]
Applying distributive property we have:
[tex]x ^ 2 + 3x-2x-6 = 0\\x ^ 2 + x-6 = 0[/tex]
Now, if we multiply both sides of the equation by 2, we have:
[tex]2x ^ 2 + 2x-12 = 0[/tex]
Thus, the equation that has the solution[tex]x = 2\ and\ x = -3[/tex] is:
[tex]2x ^ 2 + 2x-12 = 0[/tex]
Answer:
[tex]2x ^ 2 + 2x-12 = 0[/tex]
Option D
