Expand 2a(x+1)^2 +b(x+1) + c
Rearrange.
\\2x^2-5x+7
\\2a(x+1)^2+b(x+1)+c\\2ax^2+4ax+2a+bx+b+c\\(2a)x^2+(4a+b)x+(2a+b+c)\\\\2x^2-5x+7 \\\\ $You know that $ 2a = 2 \\ \therefore a = 1\\$You know that $ -5 = 4a + b $ \\ -5 = 4 + b \\ \therefore b = -9 \\ 7 = 2a + b + c \\ 7 = 2 - 9 + c \\ c = 14